Work

Unipotent representations of complex groups and extended Sommers duality

Year: 2025

Type: article

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 .

Source: Proceedings of the London Mathematical Society

DOI: 10.1112/plms.70035

Authors: Lucas Mason‐Brown, Dmytro Matvieievskyi, Shilin Yu

Institutions: The University of Texas at Austin, Kavli Institute for the Physics and Mathematics of the Universe, The University of Tokyo, East China Normal University

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Natural Science Foundation of Fujian Province, Fundamental Research Funds for the Central Universities

Awards: G2478177924, G3896691591, G6615420347, G8130433012