2010/06/11 by Ulrich Goertz, Goertz, Ulrich, Xuhua He +1
Mathematics · #20F55 #20G25 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:20F55 #msc:20G25
paper · pdf · doi:10.48550/arxiv.1006.2291
22 pages
arxiv created 2010/06/11 · openalex publication_date 2010/06/11 · arxiv updated 2010/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Affine Deligne-Lusztig varieties are analogs of Deligne-Lusztig varieties in the context of an affine root system. We prove a conjecture stated in the paper arXiv:0805.0045v4 by Haines, Kottwitz, Reuman, and the first named author, about the question which affine Deligne-Lusztig varieties (for a split group and a basic σ-conjugacy class) in the Iwahori case are non-empty. If the underlying algebraic group is a classical group and the chosen basic σ-conjugacy class is the class of b=1, we also prove the dimension formula predicted in op. cit. in almost all cases.