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

Schremmer, Felix

doi:10.2140/ant.2025.19.2015

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

Felix Schremmer

Vol. 19 (2025), No. 10, 2015–2047

DOI: 10.2140/ant.2025.19.2015

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.

Keywords

affine Weyl group, Iwahori-Hecke algebra, double Bruhat graph, class polynomial, structure constant, affine Deligne-Lusztig variety, Shimura variety, Langlands program

Mathematical Subject Classification

Primary: 11G25, 20C08, 20G25

Milestones

Received: 12 June 2023

Revised: 8 August 2024

Accepted: 18 October 2024

Published: 5 September 2025

Authors

Felix Schremmer
Department of Mathematics and New Cornerstone Laboratory The University of Hong Kong Hong Kong

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Vol. 19, No. 10, 2025