2021/09/03 by Alexander B. Ivanov
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Artin group #Combinatorics #Computer science #Conjugacy class #Coxeter complex #Coxeter element #Coxeter group #Decomposition #Disjoint sets #Disjoint union (topology) #Field (mathematics) #Group (periodic table) #Group theory #Mathematics #Physics #Pure mathematics #Reductive group #Section (typography) #Space (punctuation) #math.AG #math.RT #msc:14F20 #msc:14M15 #msc:20G25
paper · pdf · doi:10.46298/epiga.2023.8562
published as Épijournal de Géométrie Algébrique, Volume 7 (September 27, 2023) epiga:8562 · Épijournal de Géométrie Algébrique, Volume 7 (2023), Article no. 19
arxiv created 2023/09/26 · openalex publication_date 2023/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28 · arxiv updated 2026/08/05
We analyze the geometry of some p-adic Deligne--Lusztig spaces Xw(b) introduced in [Iva21] attached to an unramified reductive group \bf G over a non-archimedean local field. We prove that when \bf G is classical, b basic and w Coxeter, Xw(b) decomposes as a disjoint union of translates of a certain integral p-adic Deligne--Lusztig space. Along the way we extend some observations of DeBacker and Reeder on rational conjugacy classes of unramified tori to the case of extended pure inner forms, and prove a loop version of Frobenius-twisted Steinberg's cross section. Comment: 'Epijournal de G'eom'etrie Alg'ebrique, Volume 7 (2023), Article no. 19