Cordial elements and dimensions of affine Deligne-Lusztig varieties

2020/01/10 by Xuhua He, He, Xuhua
Mathematics · #14L05 #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.2001.03325

openalex publication_date 2020/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The affine Deligne-Lusztig variety X_w(b) in the affine flag variety of a reductive group \mathbb G depends on two parameters: the σ-conjugacy class [b] and the element w in the Iwahori-Weyl group W of \mathbb G. In this paper, for any given σ-conjugacy class [b], we determine the nonemptiness pattern and the dimension formula of X_w(b) for most w ∈ W.

Citations

• A guide to the reduction modulo p of Shimura varieties

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• Affine Deligne-Lusztig varieties via the double Bruhat graph II: Iwahori-Hecke algebra
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