Work

Genuine Gelfand–Graev functor and the quantum affine Schur–Weyl duality

Year: 2025

Type: article

Abstract: We explicate relations among the Gelfand–Graev modules for central covers of reductive p-adic groups, the Euler–Poincaré polynomial of the Arnold–Brieskorn manifold, and the quantum affine Schur–Weyl duality. These three objects and their relations are dictated by a permutation representation of the Weyl group. Our main result concerns the connection between the Gelfand–Graev module and quantum affine Schur-Weyl duality, which only holds for certain covers of $$\textrm{GL}(r)$$ GL ( r ) . In this case, the Gelfand–Graev functor is essentially the quantum affine Schur–Weyl functor. This has two significant consequences. First, the commuting algebra of the Iwahori-fixed part of the Gelfand–Graev representation is the quotient of a quantum group. Second, intertwining operators on the p-adic group side are matched with R-matrices on the quantum group side, reproving a result of Brubaker–Buciumas–Bump.

Source: Selecta Mathematica

DOI: 10.1007/s00029-025-01049-2

Authors: Fan Gao, Nadya Gurevich, Edmund Karasiewicz

Institutions: Zhejiang University, Ben-Gurion University of the Negev, National University of Singapore

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: National Natural Science Foundation of China, Israel Science Foundation, Ben-Gurion University of the Negev