Partition complexes, duality and integral tree representations

Details Partition complexes, duality and integral tree representations Partition complexes, duality and integral tree representations

2004-10-26

arxiv.org/abs/math/0410555v1

Algebr. Geom. Topol. 4 (2004) 943-960

Mathematics

Category Theory

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

Scientific paper

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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