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May 2020 Arthur parameters and cuspidal automorphic modules of classical groups
Dihua Jiang, Lei Zhang
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Ann. of Math. (2) 191(3): 739-827 (May 2020). DOI: 10.4007/annals.2020.191.3.2

Abstract

The endoscopic classification via the stable trace formula comparison provides certain character relations between irreducible cuspidal automorphic representations of classical groups and their global Arthur parameters, which are certain automorphic representations of general linear groups. It is a question of J. Arthur and W. Schmid that asks how to construct concrete modules for irreducible cuspidal automorphic representations of classical groups in term of their global Arthur parameters? In this paper, we formulate a general construction of concrete modules, using Bessel periods, for cuspidal automorphic representations of classical groups with generic global Arthur parameters. Then we establish the theory for orthogonal and unitary groups, based on certain well expected conjectures. Among the consequences of the theory in this paper is that the global Gan-Gross-Prasad conjecture for those classical groups is proved in full generality in one direction and with a global assumption in the other direction.

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Dihua Jiang. Lei Zhang. "Arthur parameters and cuspidal automorphic modules of classical groups." Ann. of Math. (2) 191 (3) 739 - 827, May 2020. https://doi.org/10.4007/annals.2020.191.3.2

Information

Published: May 2020
First available in Project Euclid: 21 December 2021

Digital Object Identifier: 10.4007/annals.2020.191.3.2

Subjects:
Primary: 11F70 , 22E50
Secondary: 11F85 , 22E55

Keywords: Arthur parameters , Bessel-Fourier coefficients , classical groups , cuspidal automorphic modules , global Gan-Gross-Prasad conjecture , twisted automorphic descent

Rights: Copyright © 2020 Department of Mathematics, Princeton University

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Vol.191 • No. 3 • May 2020
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