Eric Babson ; Victor Reiner - Coxeter-like complexes

dmtcs:312 - Discrete Mathematics & Theoretical Computer Science, January 1, 2004, Vol. 6 no. 2 - https://doi.org/10.46298/dmtcs.312
Coxeter-like complexesArticle

Authors: Eric Babson 1; Victor Reiner 2

  • 1 Department of Mathematics [Seattle]
  • 2 School of Mathematics

Motivated by the Coxeter complex associated to a Coxeter system (W,S), we introduce a simplicial regular cell complex Δ (G,S) with a G-action associated to any pair (G,S) where G is a group and S is a finite set of generators for G which is minimal with respect to inclusion. We examine the topology of Δ (G,S), and in particular the representations of G on its homology groups. We look closely at the case of the symmetric group S_n minimally generated by (not necessarily adjacent) transpositions, and their type-selected subcomplexes. These include not only the Coxeter complexes of type A, but also the well-studied chessboard complexes.


Volume: Vol. 6 no. 2
Published on: January 1, 2004
Imported on: March 26, 2015
Keywords: Coxeter complex,simplicial poset,Boolean complex,chessboard complex,Shephard group,unitary reflection group,simplex of groups,homology representation,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • Combinatorics and Topology of Simplicial Complexes; Funder: National Science Foundation; Code: 9877047
  • Combinatorial Intersection Theory; Funder: National Science Foundation; Code: 0070571

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