Level One Algebraic Cusp Forms of Classical Groups of Small Rank

Gaetan Chenevier and David A. Renard, Centre de Mathematiques Laurent Schwartz, Ecole Polytechnique, Palaiseau, France.

Introduction Polynomial invariants of finite subgroups of compact connected Lie groups
Automorphic representations of classical groups : review of Arthur's results
Determination of $/Pi_/mathrm{alg}^/bot(/mathrm{PGL}_n)$ for $n/leq 5$
Description of $/Pi_/mathrm{disc}(/mathrm{SO}_7)$ and $/Pi_/mathrm{alg}^{/mathrm s}(/mathrm{PGL}_6)$
Description of $/Pi_/mathrm{disc}({/mathrm SO}_9)$ and $/Pi_/mathrm{alg}^{/mathrm s}(/mathrm{PGL}_8)$
Description of $/Pi_/mathrm{disc}(/mathrm{SO}_8)$ and $/Pi_/mathrm{alg}^{/mathrm o}(/mathrm{PGL}_8)$
Description of $/Pi_/mathrm{disc}({/mathrm G}_2)$
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 ${/mathrm SO}_{25}$ with trivial coefficients
Bibliography