Level one algebraic cusp forms of classical groups of small rank

Level one algebraic cusp forms of classical groups of small rank / Gaëtan Chenevier, David Renard.

The authors determine the number of level 1, polarized, algebraic regular, cuspidal automorphic representations of \mathrm{GL}_n over \mathbb Q of any given infinitesimal character, for essentially all n \leq 8. For this, they compute the dimensions of spaces of level 1 automorphic forms for certain...

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Bibliographic Details
Main Authors: Chenevier, Gaëtan (Author), Renard, David, 1968- (Author)
Format: eBook
Language:English
Published: Providence, Rhode Island : American Mathematical Society, 2015.
Series:Memoirs of the American Mathematical Society ; no. 1121.
Subjects:
Forms (Mathematics)
Cusp forms (Mathematics)
Online Access:Click for online access
Table of Contents:
  • Chapter 1. Introduction Chapter 2. Polynomial invariants of finite subgroups of compact connected Lie groups Chapter 3. Automorphic representations of classical groups : review of Arthur's results Chapter 4. Determination of $\Pi _{\rm alg}^\bot ({\rm PGL}_n)$ for $n\leq 5$ Chapter 5. Description of $\Pi _{\rm disc}({\rm SO}_7)$ and $\Pi _{\rm alg}^{\rm s}({\rm PGL}_6)$ Chapter 6. Description of $\Pi _{\rm disc}({\rm SO}_9)$ and $\Pi _{\rm alg}^{\rm s}({\rm PGL}_8)$ Chapter 7. Description of $\Pi _{\rm disc}({\rm SO}_8)$ and $\Pi _{\rm alg}^{\rm o}({\rm PGL}_8)$ Chapter 8. Description of $\Pi _{\rm disc}({\rm G}_2)$ Chapter 9. Application to Siegel modular forms Appendix A. Adams-Johnson packets Appendix B. The Langlands group of $\mathbb {Z}$ and Sato-Tate groups Appendix C. Tables Appendix D. The $121$ level $1$ automorphic representations of ${\rm SO}_{25}$ with trivial coefficients.

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