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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...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore ; Hackensack, N.J. :
World Scientific,
©2006.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.
- 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.