On the complementary Arthur representations and unitary dual for p-adic classical groups

2025/05/16 by Alexander Hazeltine, Dihua Jiang, Hazeltine, Alexander +7
Mathematics · #math.RT #math.NT

paper · pdf · doi:10.48550/arxiv.2505.11381

Abstract

In [HJLLZ24], we proposed a new conjecture on the structure of the unitary dual of connected reductive groups over non-Archimedean local fields of characteristic zero based on their Arthur representations and verified it for all the known cases on the unitary dual problem. One step towards this conjecture involves the question whether certain complementary Arthur representations are unitary. In this paper, we give an explicit characterization of the complementary Arthur representations for symplectic and split odd special orthogonal groups. As applications, we obtain interesting constraints on local components of irreducible self-dual cuspidal automorphic representations of GL_N, especially when N=2,3.

Citations

• Local Intertwining Relations and Co-tempered A-packets of Classical Groups
• Une preuve simple des conjectures de Langlands pour GL(n) sur un corps p-adique

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