Linear and projective representations of symmetric groups:
The representation theory of symmetric groups is one of the most beautiful, popular and important parts of algebra, with many deep relations to other areas of mathematics such as combinatories, Lie theory and algebraic geometry. Kleshchev describes a new approach to the subject, based on the recent...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2005
|
| Series: | Cambridge tracts in mathematics
163 |
| Subjects: | |
| Online Access: | BSB01 FHN01 UBR01 Volltext |
| Summary: | The representation theory of symmetric groups is one of the most beautiful, popular and important parts of algebra, with many deep relations to other areas of mathematics such as combinatories, Lie theory and algebraic geometry. Kleshchev describes a new approach to the subject, based on the recent work of Lascoux, Leclerc, Thibon, Ariki, Grojnowski and Brundan, as well as his own. Much of this work has previously appeared only in the research literature. However to make it accessible to graduate students, the theory is developed from scratch, the only prerequisite being a standard course in abstract algebra. For the sake of transparency, Kleshchev concentrates on symmetric and spin-symmetric groups, though methods he develops are quite general and apply to a number of related objects. In sum, this unique book will be welcomed by graduate students and researchers as a modern account of the subject |
| Physical Description: | 1 Online-Ressource (xiv, 277 Seiten) |
| ISBN: | 9780511542800 |
| DOI: | 10.1017/CBO9780511542800 |
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| 505 | 8 | 0 | |g 1 |t Notation and generalities |g 2 |t Symmetric groups I |g 3 |t Degenerate affine Hecke algebra |g 4 |t First results on H[subscript n]-modules |g 5 |t Crystal operators |g 6 |t Character calculations |g 7 |t Integral representations and cyclotomic Hecke algebras |g 8 |t Functors e[subscript i][superscript [lambda]] and f[subscript i][superscript [lambda]] |g 9 |t Construction of U[subscript z][superscript +] and irreducible modules |g 10 |t Identification of the crystal |g 11 |t Symmetric groups II |g 12 |t Generalities on superalgebra |g 13 |t Sergeev superalgebras |g 14 |t Affine Sergeev superalgebras |g 15 |t Integral representations and cyclotomic Sergeev algebras |g 16 |t First results on X[subscript n]-modules |g 17 |t Crystal operators for X[subscript n] |g 18 |t Character calculations for X[subscript n] |g 19 |t Operators e[subscript i][superscript [lambda]] and f[subscript i][superscript [lambda]] |g 20 |t Construction of U[subscript z][superscript +] and irreducible modules |g 21 |t Identification of the crystal |g 22 |t Double covers |
| 520 | |a The representation theory of symmetric groups is one of the most beautiful, popular and important parts of algebra, with many deep relations to other areas of mathematics such as combinatories, Lie theory and algebraic geometry. Kleshchev describes a new approach to the subject, based on the recent work of Lascoux, Leclerc, Thibon, Ariki, Grojnowski and Brundan, as well as his own. Much of this work has previously appeared only in the research literature. However to make it accessible to graduate students, the theory is developed from scratch, the only prerequisite being a standard course in abstract algebra. For the sake of transparency, Kleshchev concentrates on symmetric and spin-symmetric groups, though methods he develops are quite general and apply to a number of related objects. In sum, this unique book will be welcomed by graduate students and researchers as a modern account of the subject | ||
| 650 | 4 | |a Symmetry groups | |
| 650 | 4 | |a Representations of groups | |
| 650 | 4 | |a Modular representations of groups | |
| 650 | 4 | |a Hecke algebras | |
| 650 | 4 | |a Superalgebras | |
| 650 | 4 | |a Linear algebraic groups | |
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| 650 | 4 | |a Geometry, Projective | |
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Record in the Search Index
| _version_ | 1804176885010137088 |
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| any_adam_object | |
| author | Kleščev, Aleksandr S. 1966- |
| author_GND | (DE-588)136718264 |
| author_facet | Kleščev, Aleksandr S. 1966- |
| author_role | aut |
| author_sort | Kleščev, Aleksandr S. 1966- |
| author_variant | a s k as ask |
| building | Verbundindex |
| bvnumber | BV043942341 |
| classification_rvk | SK 260 |
| collection | ZDB-20-CBO |
| contents | Notation and generalities Symmetric groups I Degenerate affine Hecke algebra First results on H[subscript n]-modules Crystal operators Character calculations Integral representations and cyclotomic Hecke algebras Functors e[subscript i][superscript [lambda]] and f[subscript i][superscript [lambda]] Construction of U[subscript z][superscript +] and irreducible modules Identification of the crystal Symmetric groups II Generalities on superalgebra Sergeev superalgebras Affine Sergeev superalgebras Integral representations and cyclotomic Sergeev algebras First results on X[subscript n]-modules Crystal operators for X[subscript n] Character calculations for X[subscript n] Operators e[subscript i][superscript [lambda]] and f[subscript i][superscript [lambda]] Double covers |
| ctrlnum | (ZDB-20-CBO)CR9780511542800 (OCoLC)850164220 (DE-599)BVBBV043942341 |
| dewey-full | 512.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.5 |
| dewey-search | 512.5 |
| dewey-sort | 3512.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511542800 |
| format | Electronic eBook |
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| id | DE-604.BV043942341 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9780511542800 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351311 |
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| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR |
| physical | 1 Online-Ressource (xiv, 277 Seiten) |
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| publishDate | 2005 |
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| spelling | Kleščev, Aleksandr S. 1966- Verfasser (DE-588)136718264 aut Linear and projective representations of symmetric groups Alexander Kleshchev Linear & Projective Representations of Symmetric Groups Cambridge Cambridge University Press 2005 1 Online-Ressource (xiv, 277 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 163 1 Notation and generalities 2 Symmetric groups I 3 Degenerate affine Hecke algebra 4 First results on H[subscript n]-modules 5 Crystal operators 6 Character calculations 7 Integral representations and cyclotomic Hecke algebras 8 Functors e[subscript i][superscript [lambda]] and f[subscript i][superscript [lambda]] 9 Construction of U[subscript z][superscript +] and irreducible modules 10 Identification of the crystal 11 Symmetric groups II 12 Generalities on superalgebra 13 Sergeev superalgebras 14 Affine Sergeev superalgebras 15 Integral representations and cyclotomic Sergeev algebras 16 First results on X[subscript n]-modules 17 Crystal operators for X[subscript n] 18 Character calculations for X[subscript n] 19 Operators e[subscript i][superscript [lambda]] and f[subscript i][superscript [lambda]] 20 Construction of U[subscript z][superscript +] and irreducible modules 21 Identification of the crystal 22 Double covers The representation theory of symmetric groups is one of the most beautiful, popular and important parts of algebra, with many deep relations to other areas of mathematics such as combinatories, Lie theory and algebraic geometry. Kleshchev describes a new approach to the subject, based on the recent work of Lascoux, Leclerc, Thibon, Ariki, Grojnowski and Brundan, as well as his own. Much of this work has previously appeared only in the research literature. However to make it accessible to graduate students, the theory is developed from scratch, the only prerequisite being a standard course in abstract algebra. For the sake of transparency, Kleshchev concentrates on symmetric and spin-symmetric groups, though methods he develops are quite general and apply to a number of related objects. In sum, this unique book will be welcomed by graduate students and researchers as a modern account of the subject Symmetry groups Representations of groups Modular representations of groups Hecke algebras Superalgebras Linear algebraic groups Algebras, Linear Geometry, Projective Symmetrische Gruppe (DE-588)4184204-2 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Symmetrische Gruppe (DE-588)4184204-2 s Darstellungstheorie (DE-588)4148816-7 s DE-604 Erscheint auch als Druck-Ausgabe 978-0-521-83703-3 Erscheint auch als Druck-Ausgabe 978-1-107-47164-1 https://doi.org/10.1017/CBO9780511542800 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Kleščev, Aleksandr S. 1966- Linear and projective representations of symmetric groups Notation and generalities Symmetric groups I Degenerate affine Hecke algebra First results on H[subscript n]-modules Crystal operators Character calculations Integral representations and cyclotomic Hecke algebras Functors e[subscript i][superscript [lambda]] and f[subscript i][superscript [lambda]] Construction of U[subscript z][superscript +] and irreducible modules Identification of the crystal Symmetric groups II Generalities on superalgebra Sergeev superalgebras Affine Sergeev superalgebras Integral representations and cyclotomic Sergeev algebras First results on X[subscript n]-modules Crystal operators for X[subscript n] Character calculations for X[subscript n] Operators e[subscript i][superscript [lambda]] and f[subscript i][superscript [lambda]] Double covers Symmetry groups Representations of groups Modular representations of groups Hecke algebras Superalgebras Linear algebraic groups Algebras, Linear Geometry, Projective Symmetrische Gruppe (DE-588)4184204-2 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| subject_GND | (DE-588)4184204-2 (DE-588)4148816-7 |
| title | Linear and projective representations of symmetric groups |
| title_alt | Linear & Projective Representations of Symmetric Groups Notation and generalities Symmetric groups I Degenerate affine Hecke algebra First results on H[subscript n]-modules Crystal operators Character calculations Integral representations and cyclotomic Hecke algebras Functors e[subscript i][superscript [lambda]] and f[subscript i][superscript [lambda]] Construction of U[subscript z][superscript +] and irreducible modules Identification of the crystal Symmetric groups II Generalities on superalgebra Sergeev superalgebras Affine Sergeev superalgebras Integral representations and cyclotomic Sergeev algebras First results on X[subscript n]-modules Crystal operators for X[subscript n] Character calculations for X[subscript n] Operators e[subscript i][superscript [lambda]] and f[subscript i][superscript [lambda]] Double covers |
| title_auth | Linear and projective representations of symmetric groups |
| title_exact_search | Linear and projective representations of symmetric groups |
| title_full | Linear and projective representations of symmetric groups Alexander Kleshchev |
| title_fullStr | Linear and projective representations of symmetric groups Alexander Kleshchev |
| title_full_unstemmed | Linear and projective representations of symmetric groups Alexander Kleshchev |
| title_short | Linear and projective representations of symmetric groups |
| title_sort | linear and projective representations of symmetric groups |
| topic | Symmetry groups Representations of groups Modular representations of groups Hecke algebras Superalgebras Linear algebraic groups Algebras, Linear Geometry, Projective Symmetrische Gruppe (DE-588)4184204-2 gnd Darstellungstheorie (DE-588)4148816-7 gnd |
| topic_facet | Symmetry groups Representations of groups Modular representations of groups Hecke algebras Superalgebras Linear algebraic groups Algebras, Linear Geometry, Projective Symmetrische Gruppe Darstellungstheorie |
| url | https://doi.org/10.1017/CBO9780511542800 |
| work_keys_str_mv | AT klescevaleksandrs linearandprojectiverepresentationsofsymmetricgroups AT klescevaleksandrs linearprojectiverepresentationsofsymmetricgroups |