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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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Flicker, Yuval Z. (Yuval Zvi), 1955-
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Singapore ; Hackensack, N.J. : World Scientific, ©2006.
Temas:
Acceso en línea:Texto completo

MARC

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100 1 |a Flicker, Yuval Z.  |q (Yuval Zvi),  |d 1955-  |1 https://id.oclc.org/worldcat/entity/E39PBJbWyQQwrG9ccVqhRJkdQq 
245 1 0 |a Automorphic representations of low rank groups /  |c Yuval Z. Flicker. 
260 |a Singapore ;  |a Hackensack, N.J. :  |b World Scientific,  |c ©2006. 
300 |a 1 online resource 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
504 |a Includes bibliographical references (pages 473-481) and index. 
505 0 |a Preface -- pt. 1. On the symmetric square lifting introduction. 1. Functoriality and norms. 1.1. Hecke algebra. 1.2. Norms. 1.3. Local lifting. 1.4. 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. 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. VI. 2. Proof of theorem, isotropic case. 
505 0 |a pt. 2. Automorphic representations of the unitary group U(3,E/F) 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). 1.6. Fundamental lemma again. II. Trace formula. II. 1. Stable trace formula. II. 2. Twisted trace formula. II. 3. Restricted comparison. II. 4. Trace identity. II. 5. The [symbol]-endo-lifting e'. II. 6. The quasi-endo-lifting e. II. 7. Unitary symmetric square. III. Liftings and packets. III. 1. Local identity. III. 2. Separation. III. 3. Specific lifts. III. 4. Whittaker models and twisted characters. III. 5. Global lifting. III. 6. Concluding remarks. 
500 |a Pt. 3. Zeta functions of Shimura varieties of U(3) introduction. 1. Statement of results. 2. The zeta function. I. Preliminaries. I.1. The Shumira variety. I.2. Decomposition of cohomology. I.3. Galois representations. II. Automorphic representations. II. 1. Stabilization and the test function. II. 2. Functorial overview of basechange for U(3). II. 3. Local results on basechange for U(3). II. 4. Global results on basechange for U(3). II. 5. Spectral side of the stable trace formula. II. 6. Proper endoscopic group. III. Local terms. III. 1. The reflex field. III. 2. The representation of the dual group. III. 3. Local terms at p. III. 4. The eigenvalues at p. III. 5. Terms at p for the endoscopic group. IV. Real representations. IV. 1. Representations of the real GL(2). IV. 2. Representations of U(2,l). IV. 3. Finite-dimensional representations. V. Galois representations. V.1. Stable case. V.2. Unstable case. V.3. Nontempered case. 
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. 
590 |a ProQuest Ebook Central  |b Ebook Central Academic Complete 
650 0 |a Representations of groups. 
650 0 |a Unitary groups. 
650 0 |a Lifting theory. 
650 0 |a Automorphic forms. 
650 0 |a Trace formulas. 
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 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 
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