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 Sn and Sn+1 on the homology and cohomology of this partially-ordered set.
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