Level one algebraic cusp forms of classical groups of small rank

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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Bibliographische Detailangaben
Hauptverfasser: Chenevier, Gaëtan, Renard, David
Format: E-Book Buch
Sprache:Englisch
Veröffentlicht: Providence, Rhode Island American Mathematical Society 2015
Ausgabe:1
Schriftenreihe:Memoirs of the American Mathematical Society
Schlagworte:
Cusp forms (Mathematics)
Forms (Mathematics)
euclidean lattices
classical groups
invariants of finite groups
Langlands group of <inline-formula content-type="math/mathml"> Z {\mathbb {Z}} </inline-formula>
Sato-Tate groups
conductor one
endoscopy
vector-valued Siegel modular forms
Automorphic representations
dimension formulas
compact groups
ISBN:147041094X, 9781470410940
ISSN:0065-9266, 1947-6221
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung: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 one self-dual automorphic representations of \mathrm{GL}_n with trivial infinitesimal character, and to vector valued Siegel modular forms of genus 3. A part of the authors' results are conditional to certain expected results in the theory of twisted endoscopy.
Bibliographie:Includes bibliographical references (p. 117-122)
ISBN:147041094X
9781470410940
ISSN:0065-9266
1947-6221
DOI:10.1090/memo/1121