Speaker: Prof. Alberto Minguez (University of Vienna)

Title: On the unitary dual of p-adic classical groups

Time: 15:30-16:30  August 4, 2026 (Tuesday)

Place: MCM410

Abstract: The classification of the unitary dual is one of the central problems in the representation theory of reductive p-adic groups, with applications to harmonic analysis and the theory of automorphic forms. While the case of general linear groups was settled by Tadić in the 1980s, a general description for classical groups has remained elusive.

In this talk, I will present recent joint work with Hiraku Atobe on the unitary dual of symplectic and odd orthogonal groups. We prove that every irreducible smooth representation of good parity is unitary if and only if it is of Arthur type. Our result thus connects the analytic condition of unitarity with the arithmetic notion of Arthur type, which arises from the automorphic classification of classical groups. It also provides a simple and explicit criterion for unitarity in this setting and leads to an effective algorithm for deciding whether a given representation is unitary.