Arthur parameters and cuspidal automorphic modules of classical groups

Dihua Jiang University of Minnesota Lei Zhang National University of Singapore

Number Theory Representation Theory mathscidoc:2005.24002

Gold Award Paper in 2020

Annals of Mathematics, 191, (3), 739-827, 2020
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.
Arthur parameters, Bessel-Fourier coefficients, Classical groups, cuspidal automorphic modules, global Gan-Gross-Prasad conjecture, twisted automorphic descent
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@inproceedings{dihua2020arthur,
  title={Arthur parameters and cuspidal automorphic modules of classical groups},
  author={Dihua Jiang, and Lei Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20200511220408909802670},
  booktitle={Annals of Mathematics},
  volume={191},
  number={3},
  pages={739-827},
  year={2020},
}
Dihua Jiang, and Lei Zhang. Arthur parameters and cuspidal automorphic modules of classical groups. 2020. Vol. 191. In Annals of Mathematics. pp.739-827. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20200511220408909802670.
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