English

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 RR-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