Abstract
We investigate the representation of a symmetric group Sn on the homology of its Quillen complex at a prime p. For homology groups in small codimension, we derive an explicit formula for this representation in terms of the representations of symmetric groups on homology groups of p-uniform hypergraph matching complexes. We conjecture an explicit formula for the representation of Sn on the top homology group of the corresponding hypergraph matching complex when n ≡ 1 mod p. Our conjecture follows from work of Bouc when p = 2, and we prove the conjecture when p = 3.
Original language | English (US) |
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Pages (from-to) | 2253-2271 |
Number of pages | 19 |
Journal | Journal of Algebra |
Volume | 322 |
Issue number | 7 |
DOIs | |
State | Published - Oct 1 2009 |
Keywords
- Matching complex
- Quillen complex
- Symmetric group
ASJC Scopus subject areas
- Algebra and Number Theory