Coxeter-like complexes

Eric Babson, Victor S Reiner

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

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 script G signn 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.

Original languageEnglish (US)
Pages (from-to)223-252
Number of pages30
JournalDiscrete Mathematics and Theoretical Computer Science
Volume6
Issue number2
StatePublished - Dec 1 2004

Keywords

  • Boolean complex
  • Chessboard complex
  • Coxeter complex
  • Homology representation
  • Shephard group
  • Simplex of groups
  • Simplicial poset
  • Unitary reflection group

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