Partition complexes, duality and integral tree representations

Robinson, Alan

doi:10.2140/agt.2004.4.943

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Partition complexes, duality and integral tree representations

Alan Robinson

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 ${1, 2, \dots, n}$ 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 2000

Primary: 05E25

Secondary: 17B60, 55P91

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Publication

Received: 17 February 2004

Accepted: 21 September 2004

Published: 22 October 2004

Authors

Alan Robinson
Mathematics Institute University of Warwick Coventry CV4 7AL United Kingdom

Volume 4, issue 2 (2004)