2004/08/01 by Daniel C. Reuman
Mathematics · #Advanced Algebra and Geometry #Affine transformation #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Mathematics #Pure mathematics
paper · pdf · doi:10.1307/mmj/1091112084
crossref issued 2004/08/01 · crossref published 2004/08/01 · crossref published-print 2004/08/01 · openalex publication_date 2004/08/01 · crossref created 2005/06/15 · crossref deposited 2021/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/15 · crossref indexed 2026/07/31
Rapoport and Kottwitz defined the affine Deligne-Lusztig varieties XP ˜w (bσ) of a quasisplit connected reductive group G over F = Fq((t)) for a parahoric subgroup P. They asked which pairs (b, ˜w) give non-empty varieties, and in these cases what dimensions do these varieties have. This paper answers these questions for P = I an Iwahori subgroup, in the cases b = 1, G = SL2, SL3, Sp4. This information is used to get a formula for the dimensions of the XK ˜w (σ) (all shown to be non-empty by Rapoport and Kottwitz) for the above G that supports a general conjecture of Rapoport. Here K is a special maximal compact subgroup. 1