2022/08/30 by Xuhua He, He, Xuhua, Sian Nie +3 · 1 citation
Mathematics · #11G25 #20G25 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2208.14058
openalex publication_date 2022/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study affine Deligne--Lusztig varieties Xw(b) when the finite part of the element w in the Iwahori--Weyl group is a partial σ-Coxeter element. We show that such w is a cordial element and Xw(b) ≠ ∅ if and only if b satisfies a certain Hodge--Newton indecomposability condition. The main result of this paper is that for such w and b, Xw(b) has a simple geometric structure: the σ-centralizer of b acts transitively on the set of irreducible components of Xw(b); and each irreducible component is an iterated fibration over a classical Deligne--Lusztig variety of Coxeter type, and the iterated fibers are either \mathbb A1 or \mathbb Gm.