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) |
|---|---|
| Pages (from-to) | 2253-2271 |
| Number of pages | 19 |
| Journal | Journal of Algebra |
| Volume | 322 |
| Issue number | 7 |
| DOIs | |
| State | Published - Oct 1 2009 |
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Keywords
- Matching complex
- Quillen complex
- Symmetric group
ASJC Scopus subject areas
- Algebra and Number Theory
Cite this
Top homology of hypergraph matching complexes, p-cycle complexes and Quillen complexes of symmetric groups. / Shareshian, John; Galloway, Michelle L.
In: Journal of Algebra, Vol. 322, No. 7, 01.10.2009, p. 2253-2271.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Top homology of hypergraph matching complexes, p-cycle complexes and Quillen complexes of symmetric groups
AU - Shareshian, John
AU - Galloway, Michelle L
PY - 2009/10/1
Y1 - 2009/10/1
N2 - 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.
AB - 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.
KW - Matching complex
KW - Quillen complex
KW - Symmetric group
UR - http://www.scopus.com/inward/record.url?scp=68349148210&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=68349148210&partnerID=8YFLogxK
U2 - 10.1016/j.jalgebra.2008.11.042
DO - 10.1016/j.jalgebra.2008.11.042
M3 - Article
AN - SCOPUS:68349148210
VL - 322
SP - 2253
EP - 2271
JO - Journal of Algebra
JF - Journal of Algebra
SN - 0021-8693
IS - 7
ER -