On Arthur representations and the unitary dual

2024/10/15 by Alexander Hazeltine, Dihua Jiang, Hazeltine, Alexander +7 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Finite Group Theory Research #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2410.11806

Abstract

In this paper, we propose a new conjecture describing the structure of the unitary dual in terms of Arthur representations for connected reductive algebraic groups defined over any non-Archimedean local field of characteristic zero. This conjecture provides a candidate set for the unitary dual, constructed from Arthur representations. For classical groups, we develop an explicit algorithm to generate this candidate set. Evidence for its exhaustiveness includes compatibility with the known generic unitary dual, unramified unitary dual, and low-corank representations. As further support, we verify the conjecture for the unitary dual of the exceptional group of type G₂.

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• Unitary dual of p-adic split SO_2n+1 and Sp_2n: The good parity case (and slightly beyond)

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