The good-parity Arthur-type conjecture for classical groups

Let GG be a classical group, and let Πgp(G)\Pi_{gp}(G) be the set of good-parity representations. Write ΠA,gp(G)\Pi_{A,\,gp}(G) for the good-parity Arthur representations, ΠA,gp(G)\Pi_{\overline{A},\,gp}(G) for the good-parity part of the Arthur closure, and Πu,gp(G)\Pi_{u,\,gp}(G) for the good-parity unitary representations.

Good-parity Arthur-type conjecture. For a classical group GG,

ΠA,gp(G)=ΠA,gp(G)=Πu,gp(G).\Pi_{A,\,gp}(G)=\Pi_{\overline{A},\,gp}(G)=\Pi_{u,\,gp}(G).

Equivalently, for every πΠgp(G)\pi\in\Pi_{gp}(G), π\pi is of Arthur type if and only if it is unitary. This is proposed as a representation-theoretic description of Arthur representations; its general validity is not established in the supplied text.

Sources & referencesView supporting material

Primary source

Alexander Hazeltine, Dihua Jiang, Baiying Liu, Chi-Heng Lo and Qing Zhang, “On Arthur representations and the unitary dual”, arXiv:2410.11806 (2026).

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