The multistep homology of the simplex and representations of symmetric groups

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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 languageEnglish
Pages (from-to)1-23
Number of pages23
JournalMathematical Proceedings of the Cambridge Philosophical Society
Early online date20 Jun 2019
DOIs
Publication statusE-pub ahead of print - 20 Jun 2019

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