Construction of double coset system of a Coxeter group and its\n applications to Bruhat graphs

2019/07/26 by Masato Kobayashi, Kobayashi, Masato
Mathematics · #2010 Primary:20F55 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Secondary:51F15

paper · pdf · doi:10.48550/arxiv.1907.11801

openalex publication_date 2019/07/26 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

We develop combinatorics of parabolic double cosets in finite Coxeter groups\nas a follow-up of recent articles by Billey-Konvalinka-Petersen-Slofstra-Tenner\nand Petersen. (1) We construct a double coset system as a generalization of a\ntwo-sided analogue of a Coxeter complex and present its order structure with\nits local dimension function on certain connected components. As applications\nof double cosets to Bruhat graphs, we also prove: (2) every parabolic double\ncoset is regular, (3) invariance of degree on Bruhat graph on lower intervals\nas an analogy of the one for Kazhdan-Lusztig polynomials, (4) every noncritical\nBruhat interval satisfies out-Eulerian property.\n

Related

• Bruhat order and graph structures of lower intervals in Coxeter groups
• Parabolic double cosets in Coxeter groups
• The parabolic coset structure of Bruhat intervals in Coxeter groups
• A note on Bruhat order and double coset representatives
• Subexpressions and the Bruhat order for double cosets