# Discrete Mathematics & Theoretical Computer Science

## Volume 6 n° 2 (2004), pp. 223-252

author: | Eric Babson and Victor Reiner |
---|---|

title: | Coxeter-like complexes |

keywords: | Coxeter complex, simplicial poset, Boolean complex, chessboard complex, Shephard group, unitary reflection group, simplex of groups, homology representation |

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 S
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.
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reference: | Eric Babson and Victor Reiner (2004),
Coxeter-like complexes,
Discrete Mathematics and Theoretical Computer Science 6, pp. 223-252 |

bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |

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Automatically produced on Sat Jun 19 16:16:02 CEST 2004 by gustedt