Affine Deligne-Lusztig varieties via the double Bruhat graph II: Iwahori-Hecke algebra
Felix Schremmer
Published: 2023/6/12
Abstract
We introduce a new language to describe the geometry of affine Deligne-Lusztig varieties in affine flag varieties. This second part of a two paper series uses this new language, i.e. the double Bruhat graph, to describe certain structure constants of the Iwahori-Hecke algebra. As an application, we describe nonemptiness and dimension of affine Deligne-Lusztig varieties for most elements of the affine Weyl group and arbitrary $\sigma$-conjugacy classes.