Partition complexes, duality and integral tree representations

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.
Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-41.abs.html