Level One Algebraic Cusp Forms of Classical Groups of Small Rank
Author | : Gaëtan Chenevier |
Publisher | : |
Total Pages | : 122 |
Release | : 2015 |
ISBN-10 | : 1470425092 |
ISBN-13 | : 9781470425098 |
Rating | : 4/5 (098 Downloads) |
Download or read book Level One Algebraic Cusp Forms of Classical Groups of Small Rank written by Gaëtan Chenevier and published by . This book was released on 2015 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 semisimple \mathbb Z-forms of the compact groups \mathrm{SO}_7, \mathrm{SO}_8, \mathrm{SO}_9 (and {\mathrm G}_2) and determine Arthur's endoscopic partition of these spaces in all cases. They also give applications to the 121 even lattices of rank 25 and determinant 2 found by Borcherds, to level o.