The Center of the Nilcoxeter and 0-Hecke Algebras

2008/11/16 by Joelle Brichard, Brichard, Joelle
Mathematics · #16B99 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:16B99

paper · pdf · doi:10.48550/arxiv.0811.2590

28 pages, 25 figures

arxiv created 2008/11/16 · openalex publication_date 2008/11/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the dimension of the center of the 0-Hecke algebra H_n and of the Nilcoxeter algebra NC_n using a calculus of diagrams on the Möbius band. In the case of the Nilcoxeter algebra, this calculus is shown to produce a basis for Z(NC_n) and the table of multiplication in this basis is shown to be trivial. We conjecture that a basis for Z(H_n) can also be obtained in a specific way from this topological calculus.

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