Representation theory and harmonic analysis of wreath products of finite groups /:
This book presents an introduction to the representation theory of wreath products of finite groups and harmonic analysis on the corresponding homogeneous spaces. The reader will find a detailed description of the theory of induced representations and Clifford theory, focusing on a general formulati...
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| Hauptverfasser: | , , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge :
Cambridge University Press,
2014.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
410. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book presents an introduction to the representation theory of wreath products of finite groups and harmonic analysis on the corresponding homogeneous spaces. The reader will find a detailed description of the theory of induced representations and Clifford theory, focusing on a general formulation of the little group method. This provides essential tools for the determination of all irreducible representations of wreath products of finite groups. The exposition also includes a detailed harmonic analysis of the finite lamplighter groups, the hyperoctahedral groups, and the wreath product of two symmetric groups. This relies on the generalised Johnson scheme, a new construction of finite Gelfand pairs. The exposition is completely self-contained and accessible to anyone with a basic knowledge of representation theory. Plenty of worked examples and several exercises are provided, making this volume an ideal textbook for graduate students. It also represents a useful reference for more experienced researchers. |
| Beschreibung: | 1 online resource (xii, 163 pages) |
| Bibliographie: | Includes bibliographical references (pages 157-160) and index. |
| ISBN: | 9781107732292 1107732298 9781107279087 1107279089 1139895443 9781139895446 1107721245 9781107721241 1107730546 9781107730540 1107724171 9781107724174 1107728789 9781107728783 |
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| 245 | 1 | 0 | |a Representation theory and harmonic analysis of wreath products of finite groups / |c Tullio Ceccherini-Silberstein, Fabio Scarabotti, and Filippo Tolli. |
| 264 | 1 | |a Cambridge : |b Cambridge University Press, |c 2014. | |
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| 490 | 1 | |a London Mathematical Society lecture note series ; |v 410 | |
| 504 | |a Includes bibliographical references (pages 157-160) and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |6 880-01 |a 1. General theory: 1.1. Induced representations; 1.1.1. Definitions; 1.1.2. Transitivity and additivity of induction; 1.1.3. Frobenius character formula; 1.1.4. Induction and restriction; 1.1.5. Induced representations and induced operators; 1.1.6. Frobenius reciprocity; 1.2. Harmonic analysis on a finite homogeneous space; 1.2.1. Frobenius reciprocity for permutation representations; 1.2.2. Spherical functions; 1.2.3. The other side of Frobenius reciprocity for permutation representations; 1.2.4. Gelfand pairs; 1.3. Clifford theory; 1.3.1. Clifford correspondence; 1.3.2. The little group method; 1.3.3. Semidirect products; 1.3.4. Semidirect products with an Abelian normal subgroup; 1.3.5. The affine group over a finite field; 1.3.6. The finite Heisenberg group -- 2. Wreath products of finite groups and their representation theory: 2.1. Basic properties of wreath products of finite groups; 2.1.1. Definitions; 2.1.2. Composition and exponentiation actions; 2.1.3. Iterated wreath products and their actions on rooted trees; 2.1.4. Spherically homogeneous rooted trees and their automorphism group; 2.1.5. The finite ultrametric space; 2.2. Two applications of wreath products to group theory2.2.1. The theorem of Kaloujnine and Krasner; 2.2.2. Primitivity of the exponentiation action; 2.3. Conjugacy classes of wreath products; 2.3.1. A general description of conjugacy classes; 2.3.2. Conjugacy classes of groups of the form C[sub(2)] wr G; 2.3.3. Conjugacy classes of groups of the form F wr S[sub(n)]; 2.4. Representation theory of wreath products; 2.4.1. The irreducible representations of wreath products; 2.4.2. The character and matrix coefficients of the representation tilde sigma. | |
| 505 | 8 | |a 2.5. Representation theory of groups of the form C[sub(2)] wr G2.5.1 Representation theory of the finite lamplighter group C[sub(2)] wr C[sub(n)]; 2.5.2. Representation theory of the hyperoctahedral group C[sub(2)] wr S[sub(n)]; 2.6. Representation theory of groups of the form F wr S[sub(n)]; 2.6.1. Representation theory of S[sub(m)] wr S[sub(n)] -- 3. Harmonic analysis on some homogeneous spaces of finite wreath products: 3.1. Harmonic analysis on the composition of two permutation representations; 3.1.1. Decomposition into irreducible representations; 3.1.2. Spherical matrix coefficients; 8 3.2. The generalized Johnson scheme; 3.2.1. The Johnson scheme; 3.2.2. The homogeneous space Theta h; 3.2.3. Two special kinds of tensor product; 3.2.4. The decomposition of L (Theta [sub(h)]) into irreducible representations; 3.2.5. The spherical functions; 3.2.6. The homogeneous space V(r, s) and the associated Gelfand pair; 3.3. Harmonic analysis on exponentiations and on wreath products of permutation representations; 3.3.1. Exponentiation and wreath products; 3.3.2. The case G=C[sub(2)] and Z trivial; 3.3.3. The case when L(Y) is multiplicity free; 3.3.4. Exponentiation of finite Gelfand pairs; 3.4. Harmonic analysis on finite lamplighter spaces; 3.4.1. Finite lamplighter spaces; 3.4.2. Spectral analysis of an invariant graphs; 3.4.4. The lamplighter on the complete graph. | |
| 520 | |a This book presents an introduction to the representation theory of wreath products of finite groups and harmonic analysis on the corresponding homogeneous spaces. The reader will find a detailed description of the theory of induced representations and Clifford theory, focusing on a general formulation of the little group method. This provides essential tools for the determination of all irreducible representations of wreath products of finite groups. The exposition also includes a detailed harmonic analysis of the finite lamplighter groups, the hyperoctahedral groups, and the wreath product of two symmetric groups. This relies on the generalised Johnson scheme, a new construction of finite Gelfand pairs. The exposition is completely self-contained and accessible to anyone with a basic knowledge of representation theory. Plenty of worked examples and several exercises are provided, making this volume an ideal textbook for graduate students. It also represents a useful reference for more experienced researchers. | ||
| 546 | |a English. | ||
| 650 | 0 | |a Harmonic analysis. |0 http://id.loc.gov/authorities/subjects/sh85058939 | |
| 650 | 0 | |a Finite groups. |0 http://id.loc.gov/authorities/subjects/sh85048354 | |
| 650 | 2 | |a Fourier Analysis |0 https://id.nlm.nih.gov/mesh/D005583 | |
| 650 | 6 | |a Analyse harmonique. | |
| 650 | 6 | |a Groupes finis. | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Intermediate. |2 bisacsh | |
| 650 | 7 | |a Grupos finitos |2 embne | |
| 650 | 7 | |a Análisis armónico |2 embne | |
| 650 | 7 | |a Finite groups |2 fast | |
| 650 | 7 | |a Harmonic analysis |2 fast | |
| 700 | 1 | |a Scarabotti, Fabio, |e author. |0 http://id.loc.gov/authorities/names/nb2008004991 | |
| 700 | 1 | |a Tolli, Filippo, |d 1968- |e author. |1 https://id.oclc.org/worldcat/entity/E39PCjvPB6mTJG8DYqqk3xjhDy |0 http://id.loc.gov/authorities/names/no96055886 | |
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| 830 | 0 | |a London Mathematical Society lecture note series ; |v 410. |0 http://id.loc.gov/authorities/names/n42015587 | |
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| 880 | 0 | 0 | |6 505-01/(S |g Machine generated contents note: |g 1. |t General theory -- |g 1.1. |t Induced representations -- |g 1.1.1. |t Definitions -- |g 1.1.2. |t Transitivity and additivity of induction -- |g 1.1.3. |t Frobenius character formula -- |g 1.1.4. |t Induction and restriction -- |g 1.1.5. |t Induced representations and induced operators -- |g 1.1.6. |t Frobenius reciprocity -- |g 1.2. |t Harmonic analysis on a finite homogeneous space -- |g 1.2.1. |t Frobenius reciprocity for permutation representations -- |g 1.2.2. |t Spherical functions -- |g 1.2.3. |t other side of Frobenius reciprocity for permutation representations -- |g 1.2.4. |t Gelfand pairs -- |g 1.3. |t Clifford theory -- |g 1.3.1. |t Clifford correspondence -- |g 1.3.2. |t little group method -- |g 1.3.3. |t Semidirect products -- |g 1.3.4. |t Semidirect products with an Abelian normal subgroup -- |g 1.3.5. |t affine group over a finite field -- |g 1.3.6. |t finite Heisenberg group -- |g 2. |t Wreath products of finite groups and their representation theory -- |g 2.1. |t Basic properties of wreath products of finite groups -- |g 2.1.1. |t Definitions -- |g 2.1.2. |t Composition and exponentiation actions -- |g 2.1.3. |t Iterated wreath products and their actions on rooted trees -- |g 2.1.4. |t Spherically homogeneous rooted trees and their automorphism group -- |g 2.1.5. |t finite ultrametric space -- |g 2.2. |t Two applications of wreath products to group theory -- |g 2.2.1. |t theorem of Kaloujnine and Krasner -- |g 2.2.2. |t Primitivity of the exponentiation action -- |g 2.3. |t Conjugacy classes of wreath products -- |g 2.3.1. |t general description of conjugacy classes -- |g 2.3.2. |t Conjugacy classes of groups of the form C2 G -- |g 2.3.3. |t Conjugacy classes of groups of the form F Sn -- |g 2.4. |t Representation theory of wreath products -- |g 2.4.1. |t irreducible representations of wreath products -- |g 2.4.2. |t character and matrix coefficients of the representation σ -- |g 2.5. |t Representation theory of groups of the form C2 G -- |g 2.5.1. |t Representation theory of the finite lamplighter group C2 Cn -- |g 2.5.2. |t Representation theory of the hyperoctahedral group C2 Sn -- |g 2.6. |t Representation theory of groups of the form F Sn -- |g 2.6.1. |t Representation theory of Sm Sn -- |g 3. |t Harmonic analysis on some homogeneous spaces of finite wreath products -- |g 3.1. |t Harmonic analysis on the composition of two permutation representations -- |g 3.1.1. |t Decomposition into irreducible representations -- |g 3.1.2. |t Spherical matrix coefficients -- |g 3.2. |t generalized Johnson scheme -- |g 3.2.1. |t Johnson scheme -- |g 3.2.2. |t homogeneous space h -- |g 3.2.3. |t Two special kinds of tensor product -- |g 3.2.4. |t decomposition of L(h) into irreducible representations -- |g 3.2.5. |t spherical functions -- |g 3.2.6. |t homogeneous space V(r, s) and the associated Gelfand pair -- |g 3.3. |t Harmonic analysis on exponentiations and on wreath products of permutation representations -- |g 3.3.1. |t Exponentiation and wreath products -- |g 3.3.2. |t case G = C2 and Z trivial -- |g 3.3.3. |t case when L(Y) is multiplicity free -- |g 3.3.4. |t Exponentiation of finite Gelfand pairs -- |g 3.4. |t Harmonic analysis on finite lamplighter spaces -- |g 3.4.1. |t Finite lamplighter spaces -- |g 3.4.2. |t Spectral analysis of an invariant operator -- |g 3.4.3. |t Spectral analysis of lamplighter graphs -- |g 3.4.4. |t lamplighter on the complete graph. |
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| _version_ | 1813903637625176064 |
| adam_text | |
| any_adam_object | |
| author | Ceccherini-Silberstein, Tullio Scarabotti, Fabio Tolli, Filippo, 1968- |
| author_GND | http://id.loc.gov/authorities/names/nb2008004989 http://id.loc.gov/authorities/names/nb2008004991 http://id.loc.gov/authorities/names/no96055886 |
| author_facet | Ceccherini-Silberstein, Tullio Scarabotti, Fabio Tolli, Filippo, 1968- |
| author_role | aut aut aut |
| author_sort | Ceccherini-Silberstein, Tullio |
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| collection | ZDB-4-EBA |
| contents | 1. General theory: 1.1. Induced representations; 1.1.1. Definitions; 1.1.2. Transitivity and additivity of induction; 1.1.3. Frobenius character formula; 1.1.4. Induction and restriction; 1.1.5. Induced representations and induced operators; 1.1.6. Frobenius reciprocity; 1.2. Harmonic analysis on a finite homogeneous space; 1.2.1. Frobenius reciprocity for permutation representations; 1.2.2. Spherical functions; 1.2.3. The other side of Frobenius reciprocity for permutation representations; 1.2.4. Gelfand pairs; 1.3. Clifford theory; 1.3.1. Clifford correspondence; 1.3.2. The little group method; 1.3.3. Semidirect products; 1.3.4. Semidirect products with an Abelian normal subgroup; 1.3.5. The affine group over a finite field; 1.3.6. The finite Heisenberg group -- 2. Wreath products of finite groups and their representation theory: 2.1. Basic properties of wreath products of finite groups; 2.1.1. Definitions; 2.1.2. Composition and exponentiation actions; 2.1.3. Iterated wreath products and their actions on rooted trees; 2.1.4. Spherically homogeneous rooted trees and their automorphism group; 2.1.5. The finite ultrametric space; 2.2. Two applications of wreath products to group theory2.2.1. The theorem of Kaloujnine and Krasner; 2.2.2. Primitivity of the exponentiation action; 2.3. Conjugacy classes of wreath products; 2.3.1. A general description of conjugacy classes; 2.3.2. Conjugacy classes of groups of the form C[sub(2)] wr G; 2.3.3. Conjugacy classes of groups of the form F wr S[sub(n)]; 2.4. Representation theory of wreath products; 2.4.1. The irreducible representations of wreath products; 2.4.2. The character and matrix coefficients of the representation tilde sigma. 2.5. Representation theory of groups of the form C[sub(2)] wr G2.5.1 Representation theory of the finite lamplighter group C[sub(2)] wr C[sub(n)]; 2.5.2. Representation theory of the hyperoctahedral group C[sub(2)] wr S[sub(n)]; 2.6. Representation theory of groups of the form F wr S[sub(n)]; 2.6.1. Representation theory of S[sub(m)] wr S[sub(n)] -- 3. Harmonic analysis on some homogeneous spaces of finite wreath products: 3.1. Harmonic analysis on the composition of two permutation representations; 3.1.1. Decomposition into irreducible representations; 3.1.2. Spherical matrix coefficients; 8 3.2. The generalized Johnson scheme; 3.2.1. The Johnson scheme; 3.2.2. The homogeneous space Theta h; 3.2.3. Two special kinds of tensor product; 3.2.4. The decomposition of L (Theta [sub(h)]) into irreducible representations; 3.2.5. The spherical functions; 3.2.6. The homogeneous space V(r, s) and the associated Gelfand pair; 3.3. Harmonic analysis on exponentiations and on wreath products of permutation representations; 3.3.1. Exponentiation and wreath products; 3.3.2. The case G=C[sub(2)] and Z trivial; 3.3.3. The case when L(Y) is multiplicity free; 3.3.4. Exponentiation of finite Gelfand pairs; 3.4. Harmonic analysis on finite lamplighter spaces; 3.4.1. Finite lamplighter spaces; 3.4.2. Spectral analysis of an invariant graphs; 3.4.4. The lamplighter on the complete graph. |
| ctrlnum | (OCoLC)871258013 |
| dewey-full | 512/.23 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.23 |
| dewey-search | 512/.23 |
| dewey-sort | 3512 223 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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General theory: 1.1. Induced representations; 1.1.1. Definitions; 1.1.2. Transitivity and additivity of induction; 1.1.3. Frobenius character formula; 1.1.4. Induction and restriction; 1.1.5. Induced representations and induced operators; 1.1.6. Frobenius reciprocity; 1.2. Harmonic analysis on a finite homogeneous space; 1.2.1. Frobenius reciprocity for permutation representations; 1.2.2. Spherical functions; 1.2.3. The other side of Frobenius reciprocity for permutation representations; 1.2.4. Gelfand pairs; 1.3. Clifford theory; 1.3.1. Clifford correspondence; 1.3.2. The little group method; 1.3.3. Semidirect products; 1.3.4. Semidirect products with an Abelian normal subgroup; 1.3.5. The affine group over a finite field; 1.3.6. The finite Heisenberg group -- 2. Wreath products of finite groups and their representation theory: 2.1. Basic properties of wreath products of finite groups; 2.1.1. Definitions; 2.1.2. Composition and exponentiation actions; 2.1.3. Iterated wreath products and their actions on rooted trees; 2.1.4. Spherically homogeneous rooted trees and their automorphism group; 2.1.5. The finite ultrametric space; 2.2. Two applications of wreath products to group theory2.2.1. The theorem of Kaloujnine and Krasner; 2.2.2. Primitivity of the exponentiation action; 2.3. Conjugacy classes of wreath products; 2.3.1. A general description of conjugacy classes; 2.3.2. Conjugacy classes of groups of the form C[sub(2)] wr G; 2.3.3. Conjugacy classes of groups of the form F wr S[sub(n)]; 2.4. Representation theory of wreath products; 2.4.1. The irreducible representations of wreath products; 2.4.2. The character and matrix coefficients of the representation tilde sigma.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">2.5. Representation theory of groups of the form C[sub(2)] wr G2.5.1 Representation theory of the finite lamplighter group C[sub(2)] wr C[sub(n)]; 2.5.2. Representation theory of the hyperoctahedral group C[sub(2)] wr S[sub(n)]; 2.6. Representation theory of groups of the form F wr S[sub(n)]; 2.6.1. Representation theory of S[sub(m)] wr S[sub(n)] -- 3. Harmonic analysis on some homogeneous spaces of finite wreath products: 3.1. Harmonic analysis on the composition of two permutation representations; 3.1.1. Decomposition into irreducible representations; 3.1.2. Spherical matrix coefficients; 8 3.2. The generalized Johnson scheme; 3.2.1. The Johnson scheme; 3.2.2. The homogeneous space Theta h; 3.2.3. Two special kinds of tensor product; 3.2.4. The decomposition of L (Theta [sub(h)]) into irreducible representations; 3.2.5. The spherical functions; 3.2.6. The homogeneous space V(r, s) and the associated Gelfand pair; 3.3. Harmonic analysis on exponentiations and on wreath products of permutation representations; 3.3.1. Exponentiation and wreath products; 3.3.2. The case G=C[sub(2)] and Z trivial; 3.3.3. The case when L(Y) is multiplicity free; 3.3.4. Exponentiation of finite Gelfand pairs; 3.4. Harmonic analysis on finite lamplighter spaces; 3.4.1. Finite lamplighter spaces; 3.4.2. Spectral analysis of an invariant graphs; 3.4.4. The lamplighter on the complete graph.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This book presents an introduction to the representation theory of wreath products of finite groups and harmonic analysis on the corresponding homogeneous spaces. The reader will find a detailed description of the theory of induced representations and Clifford theory, focusing on a general formulation of the little group method. This provides essential tools for the determination of all irreducible representations of wreath products of finite groups. The exposition also includes a detailed harmonic analysis of the finite lamplighter groups, the hyperoctahedral groups, and the wreath product of two symmetric groups. 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| id | ZDB-4-EBA-ocn871258013 |
| illustrated | Not Illustrated |
| indexdate | 2024-10-25T16:21:51Z |
| institution | BVB |
| isbn | 9781107732292 1107732298 9781107279087 1107279089 1139895443 9781139895446 1107721245 9781107721241 1107730546 9781107730540 1107724171 9781107724174 1107728789 9781107728783 |
| language | English |
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| owner_facet | MAIN |
| physical | 1 online resource (xii, 163 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | London Mathematical Society lecture note series ; |
| series2 | London Mathematical Society lecture note series ; |
| spelling | Ceccherini-Silberstein, Tullio, author. http://id.loc.gov/authorities/names/nb2008004989 Representation theory and harmonic analysis of wreath products of finite groups / Tullio Ceccherini-Silberstein, Fabio Scarabotti, and Filippo Tolli. Cambridge : Cambridge University Press, 2014. 1 online resource (xii, 163 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 410 Includes bibliographical references (pages 157-160) and index. Print version record. 880-01 1. General theory: 1.1. Induced representations; 1.1.1. Definitions; 1.1.2. Transitivity and additivity of induction; 1.1.3. Frobenius character formula; 1.1.4. Induction and restriction; 1.1.5. Induced representations and induced operators; 1.1.6. Frobenius reciprocity; 1.2. Harmonic analysis on a finite homogeneous space; 1.2.1. Frobenius reciprocity for permutation representations; 1.2.2. Spherical functions; 1.2.3. The other side of Frobenius reciprocity for permutation representations; 1.2.4. Gelfand pairs; 1.3. Clifford theory; 1.3.1. Clifford correspondence; 1.3.2. The little group method; 1.3.3. Semidirect products; 1.3.4. Semidirect products with an Abelian normal subgroup; 1.3.5. The affine group over a finite field; 1.3.6. The finite Heisenberg group -- 2. Wreath products of finite groups and their representation theory: 2.1. Basic properties of wreath products of finite groups; 2.1.1. Definitions; 2.1.2. Composition and exponentiation actions; 2.1.3. Iterated wreath products and their actions on rooted trees; 2.1.4. Spherically homogeneous rooted trees and their automorphism group; 2.1.5. The finite ultrametric space; 2.2. Two applications of wreath products to group theory2.2.1. The theorem of Kaloujnine and Krasner; 2.2.2. Primitivity of the exponentiation action; 2.3. Conjugacy classes of wreath products; 2.3.1. A general description of conjugacy classes; 2.3.2. Conjugacy classes of groups of the form C[sub(2)] wr G; 2.3.3. Conjugacy classes of groups of the form F wr S[sub(n)]; 2.4. Representation theory of wreath products; 2.4.1. The irreducible representations of wreath products; 2.4.2. The character and matrix coefficients of the representation tilde sigma. 2.5. Representation theory of groups of the form C[sub(2)] wr G2.5.1 Representation theory of the finite lamplighter group C[sub(2)] wr C[sub(n)]; 2.5.2. Representation theory of the hyperoctahedral group C[sub(2)] wr S[sub(n)]; 2.6. Representation theory of groups of the form F wr S[sub(n)]; 2.6.1. Representation theory of S[sub(m)] wr S[sub(n)] -- 3. Harmonic analysis on some homogeneous spaces of finite wreath products: 3.1. Harmonic analysis on the composition of two permutation representations; 3.1.1. Decomposition into irreducible representations; 3.1.2. Spherical matrix coefficients; 8 3.2. The generalized Johnson scheme; 3.2.1. The Johnson scheme; 3.2.2. The homogeneous space Theta h; 3.2.3. Two special kinds of tensor product; 3.2.4. The decomposition of L (Theta [sub(h)]) into irreducible representations; 3.2.5. The spherical functions; 3.2.6. The homogeneous space V(r, s) and the associated Gelfand pair; 3.3. Harmonic analysis on exponentiations and on wreath products of permutation representations; 3.3.1. Exponentiation and wreath products; 3.3.2. The case G=C[sub(2)] and Z trivial; 3.3.3. The case when L(Y) is multiplicity free; 3.3.4. Exponentiation of finite Gelfand pairs; 3.4. Harmonic analysis on finite lamplighter spaces; 3.4.1. Finite lamplighter spaces; 3.4.2. Spectral analysis of an invariant graphs; 3.4.4. The lamplighter on the complete graph. This book presents an introduction to the representation theory of wreath products of finite groups and harmonic analysis on the corresponding homogeneous spaces. The reader will find a detailed description of the theory of induced representations and Clifford theory, focusing on a general formulation of the little group method. This provides essential tools for the determination of all irreducible representations of wreath products of finite groups. The exposition also includes a detailed harmonic analysis of the finite lamplighter groups, the hyperoctahedral groups, and the wreath product of two symmetric groups. This relies on the generalised Johnson scheme, a new construction of finite Gelfand pairs. The exposition is completely self-contained and accessible to anyone with a basic knowledge of representation theory. Plenty of worked examples and several exercises are provided, making this volume an ideal textbook for graduate students. It also represents a useful reference for more experienced researchers. English. Harmonic analysis. http://id.loc.gov/authorities/subjects/sh85058939 Finite groups. http://id.loc.gov/authorities/subjects/sh85048354 Fourier Analysis https://id.nlm.nih.gov/mesh/D005583 Analyse harmonique. Groupes finis. MATHEMATICS Algebra Intermediate. bisacsh Grupos finitos embne Análisis armónico embne Finite groups fast Harmonic analysis fast Scarabotti, Fabio, author. http://id.loc.gov/authorities/names/nb2008004991 Tolli, Filippo, 1968- author. https://id.oclc.org/worldcat/entity/E39PCjvPB6mTJG8DYqqk3xjhDy http://id.loc.gov/authorities/names/no96055886 Print version: Ceccherini-Silberstein, Tullio. Representation theory and harmonic analysis of wreath products of finite groups 9781107627857 (DLC) 2013024946 (OCoLC)853113607 London Mathematical Society lecture note series ; 410. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=685305 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=685305 Volltext 505-01/(S Machine generated contents note: 1. General theory -- 1.1. Induced representations -- 1.1.1. Definitions -- 1.1.2. Transitivity and additivity of induction -- 1.1.3. Frobenius character formula -- 1.1.4. Induction and restriction -- 1.1.5. Induced representations and induced operators -- 1.1.6. Frobenius reciprocity -- 1.2. Harmonic analysis on a finite homogeneous space -- 1.2.1. Frobenius reciprocity for permutation representations -- 1.2.2. Spherical functions -- 1.2.3. other side of Frobenius reciprocity for permutation representations -- 1.2.4. Gelfand pairs -- 1.3. Clifford theory -- 1.3.1. Clifford correspondence -- 1.3.2. little group method -- 1.3.3. Semidirect products -- 1.3.4. Semidirect products with an Abelian normal subgroup -- 1.3.5. affine group over a finite field -- 1.3.6. finite Heisenberg group -- 2. Wreath products of finite groups and their representation theory -- 2.1. Basic properties of wreath products of finite groups -- 2.1.1. Definitions -- 2.1.2. Composition and exponentiation actions -- 2.1.3. Iterated wreath products and their actions on rooted trees -- 2.1.4. Spherically homogeneous rooted trees and their automorphism group -- 2.1.5. finite ultrametric space -- 2.2. Two applications of wreath products to group theory -- 2.2.1. theorem of Kaloujnine and Krasner -- 2.2.2. Primitivity of the exponentiation action -- 2.3. Conjugacy classes of wreath products -- 2.3.1. general description of conjugacy classes -- 2.3.2. Conjugacy classes of groups of the form C2 G -- 2.3.3. Conjugacy classes of groups of the form F Sn -- 2.4. Representation theory of wreath products -- 2.4.1. irreducible representations of wreath products -- 2.4.2. character and matrix coefficients of the representation σ -- 2.5. Representation theory of groups of the form C2 G -- 2.5.1. Representation theory of the finite lamplighter group C2 Cn -- 2.5.2. Representation theory of the hyperoctahedral group C2 Sn -- 2.6. Representation theory of groups of the form F Sn -- 2.6.1. Representation theory of Sm Sn -- 3. Harmonic analysis on some homogeneous spaces of finite wreath products -- 3.1. Harmonic analysis on the composition of two permutation representations -- 3.1.1. Decomposition into irreducible representations -- 3.1.2. Spherical matrix coefficients -- 3.2. generalized Johnson scheme -- 3.2.1. Johnson scheme -- 3.2.2. homogeneous space h -- 3.2.3. Two special kinds of tensor product -- 3.2.4. decomposition of L(h) into irreducible representations -- 3.2.5. spherical functions -- 3.2.6. homogeneous space V(r, s) and the associated Gelfand pair -- 3.3. Harmonic analysis on exponentiations and on wreath products of permutation representations -- 3.3.1. Exponentiation and wreath products -- 3.3.2. case G = C2 and Z trivial -- 3.3.3. case when L(Y) is multiplicity free -- 3.3.4. Exponentiation of finite Gelfand pairs -- 3.4. Harmonic analysis on finite lamplighter spaces -- 3.4.1. Finite lamplighter spaces -- 3.4.2. Spectral analysis of an invariant operator -- 3.4.3. Spectral analysis of lamplighter graphs -- 3.4.4. lamplighter on the complete graph. |
| spellingShingle | Ceccherini-Silberstein, Tullio Scarabotti, Fabio Tolli, Filippo, 1968- Representation theory and harmonic analysis of wreath products of finite groups / London Mathematical Society lecture note series ; 1. General theory: 1.1. Induced representations; 1.1.1. Definitions; 1.1.2. Transitivity and additivity of induction; 1.1.3. Frobenius character formula; 1.1.4. Induction and restriction; 1.1.5. Induced representations and induced operators; 1.1.6. Frobenius reciprocity; 1.2. Harmonic analysis on a finite homogeneous space; 1.2.1. Frobenius reciprocity for permutation representations; 1.2.2. Spherical functions; 1.2.3. The other side of Frobenius reciprocity for permutation representations; 1.2.4. Gelfand pairs; 1.3. Clifford theory; 1.3.1. Clifford correspondence; 1.3.2. The little group method; 1.3.3. Semidirect products; 1.3.4. Semidirect products with an Abelian normal subgroup; 1.3.5. The affine group over a finite field; 1.3.6. The finite Heisenberg group -- 2. Wreath products of finite groups and their representation theory: 2.1. Basic properties of wreath products of finite groups; 2.1.1. Definitions; 2.1.2. Composition and exponentiation actions; 2.1.3. Iterated wreath products and their actions on rooted trees; 2.1.4. Spherically homogeneous rooted trees and their automorphism group; 2.1.5. The finite ultrametric space; 2.2. Two applications of wreath products to group theory2.2.1. The theorem of Kaloujnine and Krasner; 2.2.2. Primitivity of the exponentiation action; 2.3. Conjugacy classes of wreath products; 2.3.1. A general description of conjugacy classes; 2.3.2. Conjugacy classes of groups of the form C[sub(2)] wr G; 2.3.3. Conjugacy classes of groups of the form F wr S[sub(n)]; 2.4. Representation theory of wreath products; 2.4.1. The irreducible representations of wreath products; 2.4.2. The character and matrix coefficients of the representation tilde sigma. 2.5. Representation theory of groups of the form C[sub(2)] wr G2.5.1 Representation theory of the finite lamplighter group C[sub(2)] wr C[sub(n)]; 2.5.2. Representation theory of the hyperoctahedral group C[sub(2)] wr S[sub(n)]; 2.6. Representation theory of groups of the form F wr S[sub(n)]; 2.6.1. Representation theory of S[sub(m)] wr S[sub(n)] -- 3. Harmonic analysis on some homogeneous spaces of finite wreath products: 3.1. Harmonic analysis on the composition of two permutation representations; 3.1.1. Decomposition into irreducible representations; 3.1.2. Spherical matrix coefficients; 8 3.2. The generalized Johnson scheme; 3.2.1. The Johnson scheme; 3.2.2. The homogeneous space Theta h; 3.2.3. Two special kinds of tensor product; 3.2.4. The decomposition of L (Theta [sub(h)]) into irreducible representations; 3.2.5. The spherical functions; 3.2.6. The homogeneous space V(r, s) and the associated Gelfand pair; 3.3. Harmonic analysis on exponentiations and on wreath products of permutation representations; 3.3.1. Exponentiation and wreath products; 3.3.2. The case G=C[sub(2)] and Z trivial; 3.3.3. The case when L(Y) is multiplicity free; 3.3.4. Exponentiation of finite Gelfand pairs; 3.4. Harmonic analysis on finite lamplighter spaces; 3.4.1. Finite lamplighter spaces; 3.4.2. Spectral analysis of an invariant graphs; 3.4.4. The lamplighter on the complete graph. Harmonic analysis. http://id.loc.gov/authorities/subjects/sh85058939 Finite groups. http://id.loc.gov/authorities/subjects/sh85048354 Fourier Analysis https://id.nlm.nih.gov/mesh/D005583 Analyse harmonique. Groupes finis. MATHEMATICS Algebra Intermediate. bisacsh Grupos finitos embne Análisis armónico embne Finite groups fast Harmonic analysis fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85058939 http://id.loc.gov/authorities/subjects/sh85048354 https://id.nlm.nih.gov/mesh/D005583 |
| title | Representation theory and harmonic analysis of wreath products of finite groups / |
| title_auth | Representation theory and harmonic analysis of wreath products of finite groups / |
| title_exact_search | Representation theory and harmonic analysis of wreath products of finite groups / |
| title_full | Representation theory and harmonic analysis of wreath products of finite groups / Tullio Ceccherini-Silberstein, Fabio Scarabotti, and Filippo Tolli. |
| title_fullStr | Representation theory and harmonic analysis of wreath products of finite groups / Tullio Ceccherini-Silberstein, Fabio Scarabotti, and Filippo Tolli. |
| title_full_unstemmed | Representation theory and harmonic analysis of wreath products of finite groups / Tullio Ceccherini-Silberstein, Fabio Scarabotti, and Filippo Tolli. |
| title_short | Representation theory and harmonic analysis of wreath products of finite groups / |
| title_sort | representation theory and harmonic analysis of wreath products of finite groups |
| topic | Harmonic analysis. http://id.loc.gov/authorities/subjects/sh85058939 Finite groups. http://id.loc.gov/authorities/subjects/sh85048354 Fourier Analysis https://id.nlm.nih.gov/mesh/D005583 Analyse harmonique. Groupes finis. MATHEMATICS Algebra Intermediate. bisacsh Grupos finitos embne Análisis armónico embne Finite groups fast Harmonic analysis fast |
| topic_facet | Harmonic analysis. Finite groups. Fourier Analysis Analyse harmonique. Groupes finis. MATHEMATICS Algebra Intermediate. Grupos finitos Análisis armónico Finite groups Harmonic analysis |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=685305 |
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