Volume 4, issue 2 (2004)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Partition complexes, duality and integral tree representations

Alan Robinson

Algebraic & Geometric Topology 4 (2004) 943–960

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 Σn and Σn+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