2012/01/24 by Xuhua He, He, Xuhua · 3 citations
Mathematics · #14L05 #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.1201.4901
openalex publication_date 2012/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies affine Deligne-Lusztig varieties X\tw(b) in the affine flag variety of a quasi-split tamely ramified group. We describe the geometric structure of X\tw(b) for a minimal length element \tw in the conjugacy class of an extended affine Weyl group, generalizing one of the main results in \citeHL to the affine case. We then provide a reduction method that relates the structure of X\tw(b) for arbitrary elements \tw in the extended affine Weyl group to those associated with minimal length elements. Based on this reduction, we establish a connection between the dimension of affine Deligne-Lusztig varieties and the degree of the class polynomial of affine Hecke algebras. As a consequence, we prove a conjecture of Görtz, Haines, Kottwitz and Reuman in \citeGHKR.