2012/03/21 by Xuhua He, Zhongwei Yang, He, Xuhua +1
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Representation Theory (math.RT) #math.RT
paper · pdf · doi:10.48550/arxiv.1203.4680
9 pages
arxiv created 2012/03/21 · openalex publication_date 2012/03/21 · arxiv updated 2012/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Wa be an affine Weyl group and η:Wa\longrightarrow W0 be the natural projection to the corresponding finite Weyl group. We say that w∈ Wa has finite Coxeter part if η(w) is conjugate to a Coxeter element of W0. The elements with finite Coxeter part is a union of conjugacy classes of Wa. We show that for each conjugacy class O of Wa with finite Coxeter part there exits a unique maximal proper parabolic subgroup WJ of Wa, such that the set of minimal length elements in O is exactly the set of Coxeter elements in WJ. Similar results hold for twisted conjugacy classes.