Affine Deligne-Lusztig varieties via the double Bruhat graph II: Iwahori-Hecke algebra

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.

37 pages; v2 has several corrections and updates; comments appreciated

References in corpus (2)

• Affine Bruhat order and Demazure products
• Affine Deligne-Lusztig varieties via the double Bruhat graph I: Semi-infinite orbits