The unitary dual conjecture for general connected reductive groups

From papers

Let FF be a non-Archimedean local field of characteristic zero, and let GG be a general connected reductive group defined over FF. Let ΠA(G)\Pi_A(G) denote the set of Arthur representations, and let ΠAlim(G)\Pi_{\overline{A}}^{\lim}(G) be the set obtained from them by unitary parabolic induction, complementary series, and limits of complementary series. Assume that the local Arthur conjecture holds for every Levi subgroup MM of GG. Unitary dual conjecture. The two sets are equal:

ΠAlim(G)=Πu(G).\Pi_{\overline{A}}^{\lim}(G)=\Pi_u(G).

This conjecture seeks to construct the entire unitary dual from Arthur representations using the standard unitary constructions; its resolution is not established by the supplied text.

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Sources & referencesView supporting material

Primary source

Baiying Liu, Chi-Heng Lo and Brian Wen, “On corank 4 unitary representations of classical groups”, arXiv:2603.22255 (2026).

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