Unipotent representations of complex groups and extended Sommers duality

Let (Formula presented.) be a complex reductive algebraic group. Losev, Mason-Brown, and Matvieievskyi defined a finite set of irreducible (Formula presented.) -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 (Formula presented.). In this paper, we provide a description of (some of) these representations in terms of the Langlands dual group (Formula presented.). To this end, we construct a duality map (Formula presented.) from the set of pairs (Formula presented.) consisting of a nilpotent orbit (Formula presented.) and a conjugacy class (Formula presented.) in Lusztig's canonical quotient (Formula presented.) to the set of finite covers of nilpotent orbits in (Formula presented.).