| Description |
1 online resource (xi, 485 pages) |
| 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 |
| Summary |
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] |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
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Print version record |
| Subject |
Representations of groups.
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Unitary groups.
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Lifting theory.
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Automorphic forms.
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Trace formulas.
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MATHEMATICS -- Group Theory.
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Automorphic forms
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Lifting theory
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Representations of groups
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Trace formulas
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Unitary groups
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| Form |
Electronic book
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| ISBN |
9812773622 |
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9789812773623 |
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1281924881 |
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9781281924889 |
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9786611924881 |
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6611924884 |
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