Unipotent representations of complex groups and extended Sommers duality

Abstract Let be a complex reductive algebraic group. Losev, Mason‐Brown, and Matvieievskyi defined a finite set of irreducible ‐equivariant Harish‐Chandra bimodules called unipotent representations , generalizing the special unipotent representations of Arthur and Barbasch‐Vogan. These representations are defined in terms of filtered quantizations of symplectic singularities and are expected to form the building blocks of the unitary dual of . In this paper, we provide a description of (some of) these representations in terms of the Langlands dual group . To this end, we construct a duality map from the set of pairs consisting of a nilpotent orbit and a conjugacy class in Lusztig's canonical quotient to the set of finite covers of nilpotent orbits in .