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Partition complexes, duality and integral tree representations

Alan Robinson
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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.

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Alan Robinson. 2004-10-26. Partition complexes, duality and integral tree representations. https://doi.org/10.2140/agt.2004.4.943

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