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arXiv · 1803.00465

The multistep homology of the simplex and representations of symmetric groups

Mark Wildon
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Abstract

The symmetric group on a set acts transitively on its subsets of a given size. We define homomorphisms between the corresponding permutation modules, defined over a field of characteristic two, which generalize the boundary maps from simplicial homology. The main results determine when these chain complexes are exact and when they are split exact. As a corollary we obtain a new explicit construction of the basic spin modules for the symmetric group.

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Mark Wildon. 2018-03-01. The multistep homology of the simplex and representations of symmetric groups. https://arxiv.org/abs/1803.00465

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