Modular affine Hecke category and regular unipotent centralizer, I

Roman Bezrukavnikov (1) , Simon Riche (2, 3) , Laura Rider (4)

1 MIT - Massachusetts Institute of Technology
2 LMBP - Laboratoire de Mathématiques Blaise Pascal
3 UCA [2017-2020] - Université Clermont Auvergne [2017-2020]
4 University of Georgia [USA]

In this paper we provide, under some mild explicit assumptions, a geometric description of the category of representations of the centralizer of a regular unipotent element in a reductive algebraic group in terms of perverse sheaves on the Langlands dual affine flag variety. This equivalence is suggested and motivated by the "geometric Langlands" philosophy.

Domaines: Théorie des représentations [math.RT]

Roman Bezrukavnikov, Simon Riche, Laura Rider. Modular affine Hecke category and regular unipotent centralizer, I. 2020. ⟨hal-02571688⟩