Hecke algebras and affine flag varieties in characteristic p

Tobias Schmidt (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

Let G be a split semi-simple p-adic group and let H be its Iwahori-Hecke algebra with coefficients in the algebraic closure k of the finite field with p elements. Let F be the affine flag variety over k associated with G. We show, in the simply connected simple case, that a torus-equivariant K'-theory of F (with coefficients in k) admits an H-action by Demazure operators and that this provides a model for the regular representation of H.

Domaines: Géométrie algébrique [math.AG]; Théorie des nombres [math.NT]

Tobias Schmidt. Hecke algebras and affine flag varieties in characteristic p. Journal of Pure and Applied Algebra, 2016, 220 (9), pp.3233-3247. ⟨10.1016/j.jpaa.2016.02.012⟩. ⟨hal-01318944⟩