2014/02/11 by Barbara Baumeister, Matthew S. Dyer, Baumeister, Barbara +5 · 2 citations
Mathematics · #Algebraic structures and combinatorial models #Advanced Combinatorial Mathematics #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1402.2500
In this note, we provide a short and self-contained proof that the braid\ngroup on n strands acts transitively on the set of reduced factorizations of a\nCoxeter element in a Coxeter group of finite rank n into products of\nreflections. We moreover use the same argument to also show that all\nfactorizations of an element in a parabolic subgroup of W lie as well in this\nparabolic subgroup.\n