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.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2023
- DOI:
- 10.48550/arXiv.2306.06873
- arXiv:
- arXiv:2306.06873
- Bibcode:
- 2023arXiv230606873S
- Keywords:
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- Mathematics - Representation Theory;
- Mathematics - Algebraic Geometry;
- 20G25;
- 11G25;
- 20C08
- E-Print:
- 37 pages