2023/06/09 by Felix Schremmer, Schremmer, Felix
Mathematics · #11G25 #20G25 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2306.05933
openalex publication_date 2023/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 R-polynomials. We use it to describe the geometry of many affine Deligne-Lusztig varieties, overcoming a previously ubiquitous regularity condition.