Algebraic & Geometric Topology 4 (2004) 943–960

DOI: 10.2140/agt.2004.4.943

arXiv: math.CT/0410555

Abstract

We show that the poset of non-trivial partitions of {1,2,…,n} has a fundamental homology class with coefficients in a Lie superalgebra. Homological duality then rapidly yields a range of known results concerning the integral representations of the symmetric groups Σ_n and Σ_n+1 on the homology and cohomology of this partially-ordered set.

Keywords

partition complex, Lie superalgebra

Mathematical Subject Classification

Primary: 05E25

Secondary: 17B60, 55P91

References

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Publication

Received: 17 February 2004
Accepted: 21 September 2004
Published: 22 October 2004

Authors