2009/04/11 by Xuhua He, He, Xuhua
Mathematics · #20F55 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT #msc:20F55
paper · pdf · doi:10.48550/arxiv.0904.1786
12 pages, to appear in J. Algebra
arxiv created 2009/04/11 · openalex publication_date 2009/04/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let (W, I) be a finite Coxeter group. In the case where W is a Weyl group, Berenstein and Kazhdan in \citeBK constructed a monoid structure on the set of all subsets of I using unipotent χ-linear bicrystals. In this paper, we will generalize this result to all types of finite Coxeter groups (including non-crystallographic types). Our approach is more elementary, based on some combinatorics of Coxeter groups. Moreover, we will calculate this monoid structure explicitly for each type.