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Affine Deligne-Lusztig varieties via the double Bruhat graph II: Iwahori-Hecke algebra (2306.06873v2)
Published 12 Jun 2023 in math.RT and math.AG
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.