2021/10/05 by Arghya Sadhukhan, Sadhukhan, Arghya
Mathematics · #11G25 #20F55 #20G25 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2110.02172
openalex publication_date 2021/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we consider affine Deligne-Lusztig varieties Xw(b) and their certain union X(μ,b) inside the affine flag variety of a reductive group. Several important results in the study of affine Deligne-Lusztig varieties have been established under the so-called superregularity hypothesis. Such results include a description of generic Newton points in Iwahori double cosets of loop groups, covering relation in associated Iwahori-Weyl group and dimension formula for X(μ,b). We show that one can considerably weaken the superregularity hypothesis and sometimes completely eliminate it, thus strengthening these existing results.