The multistep homology of the simplex and representations of symmetric groups

Mark Wildon

doi:10.1017/S0305004119000124

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 the set of its subsets of a fixed 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.

Original language	English
Pages (from-to)	1-23
Number of pages	23
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Early online date	20 Jun 2019
DOIs	https://doi.org/10.1017/S0305004119000124
Publication status	E-pub ahead of print - 20 Jun 2019

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10.1017/S0305004119000124

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Cite this

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