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 language | English (US) |
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Pages (from-to) | 223-252 |
Number of pages | 30 |
Journal | Discrete Mathematics and Theoretical Computer Science |
Volume | 6 |
Issue number | 2 |
State | Published - 2004 |
Keywords
- Boolean complex
- Chessboard complex
- Coxeter complex
- Homology representation
- Shephard group
- Simplex of groups
- Simplicial poset
- Unitary reflection group