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Theta correspondence and simple factors in global Arthur parameters

Chenyan Wu

Vol. 18 (2024), No. 5, 969–991
Abstract

By using results on poles of L-functions and theta correspondence, we give a bound on b for (χ,b)-factors of the global Arthur parameter of a cuspidal automorphic representation π of a classical group or a metaplectic group where χ is a conjugate self-dual automorphic character and b is an integer which is the dimension of an irreducible representation of SL 2(). We derive a more precise relation when π lies in a generic global A-packet.

Keywords
theta correspondence, Eisenstein series, $L$-functions, Arthur parameters
Mathematical Subject Classification
Primary: 11F27, 11F67, 11F70
Milestones
Received: 30 August 2022
Revised: 3 May 2023
Accepted: 20 July 2023
Published: 16 April 2024
Authors
Chenyan Wu
School of Mathematics and Statistics
University of Melbourne
Melbourne
Victoria
Australia

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