Affine Deligne-Lusztig varieties via the double Bruhat graph I: Semi-infinite orbits
Algebraic Geometry
2025-09-10 v2 Representation Theory
Abstract
We introduce a new language to describe the geometry of affine Deligne-Lusztig varieties in affine flag varieties. This first part of a two paper series develops the definition and fundamental properties of the double Bruhat graph by studying semi-infinite orbits. This double Bruhat graph was originally introduced by Naito-Watanabe to study periodic -polynomials. We use it to describe the geometry of many affine Deligne-Lusztig varieties, overcoming a previously ubiquitous regularity condition.
Keywords
Cite
@article{arxiv.2306.05933,
title = {Affine Deligne-Lusztig varieties via the double Bruhat graph I: Semi-infinite orbits},
author = {Felix Schremmer},
journal= {arXiv preprint arXiv:2306.05933},
year = {2025}
}
Comments
44 pages; many details clarified and corrected; comments appreciated