The unitary dual conjecture for classical groups

Let GnG_n be the classical group under consideration. Let ΠAlim(Gn)\Pi_{\overline{A}}^{\lim}(G_n) and ΠAlim(Gn)\Pi_{\overline{A}}^{\lim'}(G_n) denote the sets defined in the preceding discussion, where the latter allows the parameter point to lie in the closure of the relevant connected component. Unitary dual conjecture. The unitary dual is described by

ΠAlim(Gn)=ΠAlim(Gn)=Πu(Gn).\Pi_{\overline{A}}^{\lim}(G_n)=\Pi_{\overline{A}}^{\lim'}(G_n)=\Pi_u(G_n).

This conjecture asserts both that the two constructions from Arthur representations coincide and that they exhaust the unitary dual; its resolution is not established by the supplied text.

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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