Algebraic and Geometric Topology 4 (2004), paper no. 41, pages 943-960.

Partition complexes, duality and integral tree representations

Alan Robinson

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 S_n and S_{n+1} on the homology and cohomology of this partially-ordered set.

Keywords. Partition complex, Lie superalgebra

AMS subject classification. Primary: 05E25. Secondary: 17B60.

DOI: 10.2140/agt.2004.4.943

E-print: arXiv:math.CT/0410555

Submitted: 17 February 2004. Accepted: 21 September 2004. Published: 22 October 2004.

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Alan Robinson
Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK

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