Hecke action on the principal block

Roman Bezrukavnikov (1) , Simon Riche (2)

1 MIT - Massachusetts Institute of Technology
2 LMBP - Laboratoire de Mathématiques Blaise Pascal

In this paper we construct an action of the affine Hecke category on the principal block of representations of a simply-connected semisimple algebraic group over an algebraically closed field of characteristic bigger than the Coxeter number. This confirms a conjecture of G. Williamson and the second author, and provides a new proof of the tilting character formula in terms of antispherical p-Kazhdan-Lusztig polynomials.

Domaines: Théorie des représentations [math.RT]

Roman Bezrukavnikov, Simon Riche. Hecke action on the principal block. Compositio Mathematica, 2022, 158 (5), pp.953-1019. ⟨hal-02946323v2⟩