Automorphic representations of low rank groups /:
The area of automorphic representations is a natural continuation of studies in number theory and modular forms. A guiding principle is a reciprocity law relating the infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Hackensack, N.J. :
World Scientific,
©2006.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | The area of automorphic representations is a natural continuation of studies in number theory and modular forms. A guiding principle is a reciprocity law relating the infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called "liftings". This book concentrates on two initial examples: the symmetric square lifting from SL(2) to PGL(3), reflecting the 3-dimensional representation of PGL(2) in SL(3); and basechange from the unitary group U(3, E/F) to GL(3, E), [E : F]. |
| Beschreibung: | 1 online resource (xi, 485 pages) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9812773622 9789812773623 1281924881 9781281924889 9786611924881 6611924884 |
Internformat
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| 245 | 1 | 0 | |a Automorphic representations of low rank groups / |c Yuval Z. Flicker. |
| 260 | |a Hackensack, N.J. : |b World Scientific, |c ©2006. | ||
| 300 | |a 1 online resource (xi, 485 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a Cover -- CONTENTS -- PREFACE -- PART 1. ON THE SYMMETRIC SQUARE LIFTING -- INTRODUCTION -- I. FUNCTORIALITY AND NORMS -- I.1 Hecke algebra -- I.2 Norms -- I.3 Local lifting -- I.4 Orthogonality -- II. ORBITAL INTEGRALS -- II. 1 Fundamental lemma -- II. 2 Differential forms -- II. 3 Matching orbital integrals -- II. 4 Germ expansion -- III. TWISTED TRACE FORMULA -- III. 1 Geometric side -- III. 2 Analytic side -- III. 3 Trace formulae -- IV. TOTAL GLOBAL COMPARISON -- IV. 1 The comparison -- IV. 2 Appendix: Mathematica program -- V. APPLICATIONS OF A TRACE FORMULA -- V.1 Approximation -- V.2 Main theorems -- V.3 Characters and genericity -- VI. COMPUTATION OF A TWISTED CHARACTER -- VI. 1 Proof of theorem, anisotropic case 13; -- VI. 2 Proof of theorem, isotropic case -- PART 2. AUTOMORPHIC REPRESENTATIONS OF THE UNITARY GROUP U(3,E/F)13; -- INTRODUCTION -- 1. Functorial overview -- 2. Statement of results -- I. LOCAL THEORY -- I.1 Conjugacy classes -- I.2 Orbital integrals -- I.3 Fundamental lemma -- I.4 Admissible representations -- I.5 Representations of U(2,1;C/R) -- I.6 Fundamental lemma again. | |
| 588 | 0 | |a Print version record. | |
| 520 | |a The area of automorphic representations is a natural continuation of studies in number theory and modular forms. A guiding principle is a reciprocity law relating the infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called "liftings". This book concentrates on two initial examples: the symmetric square lifting from SL(2) to PGL(3), reflecting the 3-dimensional representation of PGL(2) in SL(3); and basechange from the unitary group U(3, E/F) to GL(3, E), [E : F]. | ||
| 546 | |a English. | ||
| 650 | 0 | |a Representations of groups. |0 http://id.loc.gov/authorities/subjects/sh85112944 | |
| 650 | 0 | |a Unitary groups. |0 http://id.loc.gov/authorities/subjects/sh85139728 | |
| 650 | 0 | |a Lifting theory. |0 http://id.loc.gov/authorities/subjects/sh85076864 | |
| 650 | 0 | |a Automorphic forms. |0 http://id.loc.gov/authorities/subjects/sh85010451 | |
| 650 | 0 | |a Trace formulas. |0 http://id.loc.gov/authorities/subjects/sh85136394 | |
| 650 | 6 | |a Représentations de groupes. | |
| 650 | 6 | |a Groupes unitaires. | |
| 650 | 6 | |a Relèvement (Mathématiques) | |
| 650 | 6 | |a Formes automorphes. | |
| 650 | 6 | |a Formules de trace. | |
| 650 | 7 | |a MATHEMATICS |x Group Theory. |2 bisacsh | |
| 650 | 7 | |a Automorphic forms |2 fast | |
| 650 | 7 | |a Lifting theory |2 fast | |
| 650 | 7 | |a Representations of groups |2 fast | |
| 650 | 7 | |a Trace formulas |2 fast | |
| 650 | 7 | |a Unitary groups |2 fast | |
| 776 | 0 | 8 | |i Print version: |a Flicker, Yuval Z. (Yuval Zvi), 1955- |t Automorphic representations of low rank groups. |d Hackensack, N.J. : World Scientific, ©2006 |z 9812568034 |z 9789812568038 |w (DLC) 2006283979 |w (OCoLC)71145361 |
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| adam_text | |
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| author | Flicker, Yuval Z. (Yuval Zvi), 1955- |
| author_GND | http://id.loc.gov/authorities/names/n82071071 |
| author_facet | Flicker, Yuval Z. (Yuval Zvi), 1955- |
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| contents | Cover -- CONTENTS -- PREFACE -- PART 1. ON THE SYMMETRIC SQUARE LIFTING -- INTRODUCTION -- I. FUNCTORIALITY AND NORMS -- I.1 Hecke algebra -- I.2 Norms -- I.3 Local lifting -- I.4 Orthogonality -- II. ORBITAL INTEGRALS -- II. 1 Fundamental lemma -- II. 2 Differential forms -- II. 3 Matching orbital integrals -- II. 4 Germ expansion -- III. TWISTED TRACE FORMULA -- III. 1 Geometric side -- III. 2 Analytic side -- III. 3 Trace formulae -- IV. TOTAL GLOBAL COMPARISON -- IV. 1 The comparison -- IV. 2 Appendix: Mathematica program -- V. APPLICATIONS OF A TRACE FORMULA -- V.1 Approximation -- V.2 Main theorems -- V.3 Characters and genericity -- VI. COMPUTATION OF A TWISTED CHARACTER -- VI. 1 Proof of theorem, anisotropic case 13; -- VI. 2 Proof of theorem, isotropic case -- PART 2. AUTOMORPHIC REPRESENTATIONS OF THE UNITARY GROUP U(3,E/F)13; -- INTRODUCTION -- 1. Functorial overview -- 2. Statement of results -- I. LOCAL THEORY -- I.1 Conjugacy classes -- I.2 Orbital integrals -- I.3 Fundamental lemma -- I.4 Admissible representations -- I.5 Representations of U(2,1;C/R) -- I.6 Fundamental lemma again. |
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| discipline | Mathematik |
| format | Electronic eBook |
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| indexdate | 2024-11-27T13:17:00Z |
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| publisher | World Scientific, |
| record_format | marc |
| spelling | Flicker, Yuval Z. (Yuval Zvi), 1955- https://id.oclc.org/worldcat/entity/E39PBJbWyQQwrG9ccVqhRJkdQq http://id.loc.gov/authorities/names/n82071071 Automorphic representations of low rank groups / Yuval Z. Flicker. Hackensack, N.J. : World Scientific, ©2006. 1 online resource (xi, 485 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier data file rda Includes bibliographical references and index. Cover -- CONTENTS -- PREFACE -- PART 1. ON THE SYMMETRIC SQUARE LIFTING -- INTRODUCTION -- I. FUNCTORIALITY AND NORMS -- I.1 Hecke algebra -- I.2 Norms -- I.3 Local lifting -- I.4 Orthogonality -- II. ORBITAL INTEGRALS -- II. 1 Fundamental lemma -- II. 2 Differential forms -- II. 3 Matching orbital integrals -- II. 4 Germ expansion -- III. TWISTED TRACE FORMULA -- III. 1 Geometric side -- III. 2 Analytic side -- III. 3 Trace formulae -- IV. TOTAL GLOBAL COMPARISON -- IV. 1 The comparison -- IV. 2 Appendix: Mathematica program -- V. APPLICATIONS OF A TRACE FORMULA -- V.1 Approximation -- V.2 Main theorems -- V.3 Characters and genericity -- VI. COMPUTATION OF A TWISTED CHARACTER -- VI. 1 Proof of theorem, anisotropic case 13; -- VI. 2 Proof of theorem, isotropic case -- PART 2. AUTOMORPHIC REPRESENTATIONS OF THE UNITARY GROUP U(3,E/F)13; -- INTRODUCTION -- 1. Functorial overview -- 2. Statement of results -- I. LOCAL THEORY -- I.1 Conjugacy classes -- I.2 Orbital integrals -- I.3 Fundamental lemma -- I.4 Admissible representations -- I.5 Representations of U(2,1;C/R) -- I.6 Fundamental lemma again. Print version record. The area of automorphic representations is a natural continuation of studies in number theory and modular forms. A guiding principle is a reciprocity law relating the infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called "liftings". This book concentrates on two initial examples: the symmetric square lifting from SL(2) to PGL(3), reflecting the 3-dimensional representation of PGL(2) in SL(3); and basechange from the unitary group U(3, E/F) to GL(3, E), [E : F]. English. Representations of groups. http://id.loc.gov/authorities/subjects/sh85112944 Unitary groups. http://id.loc.gov/authorities/subjects/sh85139728 Lifting theory. http://id.loc.gov/authorities/subjects/sh85076864 Automorphic forms. http://id.loc.gov/authorities/subjects/sh85010451 Trace formulas. http://id.loc.gov/authorities/subjects/sh85136394 Représentations de groupes. Groupes unitaires. Relèvement (Mathématiques) Formes automorphes. Formules de trace. MATHEMATICS Group Theory. bisacsh Automorphic forms fast Lifting theory fast Representations of groups fast Trace formulas fast Unitary groups fast Print version: Flicker, Yuval Z. (Yuval Zvi), 1955- Automorphic representations of low rank groups. Hackensack, N.J. : World Scientific, ©2006 9812568034 9789812568038 (DLC) 2006283979 (OCoLC)71145361 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=210725 Volltext |
| spellingShingle | Flicker, Yuval Z. (Yuval Zvi), 1955- Automorphic representations of low rank groups / Cover -- CONTENTS -- PREFACE -- PART 1. ON THE SYMMETRIC SQUARE LIFTING -- INTRODUCTION -- I. FUNCTORIALITY AND NORMS -- I.1 Hecke algebra -- I.2 Norms -- I.3 Local lifting -- I.4 Orthogonality -- II. ORBITAL INTEGRALS -- II. 1 Fundamental lemma -- II. 2 Differential forms -- II. 3 Matching orbital integrals -- II. 4 Germ expansion -- III. TWISTED TRACE FORMULA -- III. 1 Geometric side -- III. 2 Analytic side -- III. 3 Trace formulae -- IV. TOTAL GLOBAL COMPARISON -- IV. 1 The comparison -- IV. 2 Appendix: Mathematica program -- V. APPLICATIONS OF A TRACE FORMULA -- V.1 Approximation -- V.2 Main theorems -- V.3 Characters and genericity -- VI. COMPUTATION OF A TWISTED CHARACTER -- VI. 1 Proof of theorem, anisotropic case 13; -- VI. 2 Proof of theorem, isotropic case -- PART 2. AUTOMORPHIC REPRESENTATIONS OF THE UNITARY GROUP U(3,E/F)13; -- INTRODUCTION -- 1. Functorial overview -- 2. Statement of results -- I. LOCAL THEORY -- I.1 Conjugacy classes -- I.2 Orbital integrals -- I.3 Fundamental lemma -- I.4 Admissible representations -- I.5 Representations of U(2,1;C/R) -- I.6 Fundamental lemma again. Representations of groups. http://id.loc.gov/authorities/subjects/sh85112944 Unitary groups. http://id.loc.gov/authorities/subjects/sh85139728 Lifting theory. http://id.loc.gov/authorities/subjects/sh85076864 Automorphic forms. http://id.loc.gov/authorities/subjects/sh85010451 Trace formulas. http://id.loc.gov/authorities/subjects/sh85136394 Représentations de groupes. Groupes unitaires. Relèvement (Mathématiques) Formes automorphes. Formules de trace. MATHEMATICS Group Theory. bisacsh Automorphic forms fast Lifting theory fast Representations of groups fast Trace formulas fast Unitary groups fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85112944 http://id.loc.gov/authorities/subjects/sh85139728 http://id.loc.gov/authorities/subjects/sh85076864 http://id.loc.gov/authorities/subjects/sh85010451 http://id.loc.gov/authorities/subjects/sh85136394 |
| title | Automorphic representations of low rank groups / |
| title_auth | Automorphic representations of low rank groups / |
| title_exact_search | Automorphic representations of low rank groups / |
| title_full | Automorphic representations of low rank groups / Yuval Z. Flicker. |
| title_fullStr | Automorphic representations of low rank groups / Yuval Z. Flicker. |
| title_full_unstemmed | Automorphic representations of low rank groups / Yuval Z. Flicker. |
| title_short | Automorphic representations of low rank groups / |
| title_sort | automorphic representations of low rank groups |
| topic | Representations of groups. http://id.loc.gov/authorities/subjects/sh85112944 Unitary groups. http://id.loc.gov/authorities/subjects/sh85139728 Lifting theory. http://id.loc.gov/authorities/subjects/sh85076864 Automorphic forms. http://id.loc.gov/authorities/subjects/sh85010451 Trace formulas. http://id.loc.gov/authorities/subjects/sh85136394 Représentations de groupes. Groupes unitaires. Relèvement (Mathématiques) Formes automorphes. Formules de trace. MATHEMATICS Group Theory. bisacsh Automorphic forms fast Lifting theory fast Representations of groups fast Trace formulas fast Unitary groups fast |
| topic_facet | Representations of groups. Unitary groups. Lifting theory. Automorphic forms. Trace formulas. Représentations de groupes. Groupes unitaires. Relèvement (Mathématiques) Formes automorphes. Formules de trace. MATHEMATICS Group Theory. Automorphic forms Lifting theory Representations of groups Trace formulas Unitary groups |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=210725 |
| work_keys_str_mv | AT flickeryuvalz automorphicrepresentationsoflowrankgroups |