Hecke action on the principal block

Abstract

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. * (1) reg and g * (1) . We deduce a canonical isomorphism

A Homomorphism Between Bott–samelson Bimodules

“…An approach closer to Soergel's category was introduced in [1]. This incarnation is used by Bezrukavnikov-Riche [4] to prove a conjecture of Riche-Williamson [11] which implies the tilting character formula, and hence an irreducible character formula of algebraic representations of reductive groups when the characteristic is not too small. We remark that these categories are equivalent to each others when they behave well [1], [2], [11].…”