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 σ-conjugacy classes.
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