2024/12/06 by A. Roy Choudhury, Choudhury, Ashutosh Roy, Tanmay Deshpande +1
Physics and Astronomy · #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2412.05092
openalex publication_date 2024/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a connected reductive algebraic group over an algebraically closed field k of characteristic p > 0 and let ℓ be a prime number different from p. Let U ⊆ G be a maximal unipotent subgroup, T a maximal torus normalizing U and W the Weyl group of G. Let L be a non-degenerate multiplicative ℚℓ -local system on U. R. Bezrukavnikov and the second author have proved that the bi-Whittaker category, namely the triangulated monoidal category of (U, L)-biequivariant ℚℓ-complexes on G is monoidally equivalent to an explicit thick triangulated monoidal subcategory \mathscrDW∘(T) ⊆ \mathscrDW(T) of "central sheaves" on the torus. In particular it has the structure of a symmetric monoidal category coming from the symmetric monoidal structure on \mathscrDW(T). In this paper, we give another construction of a symmetric monoidal structure on the above category and prove that it agrees with the one coming from the above construction. For this, among other things, we generalize a proof by Gelfand for finite groups to the geometric setup.