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The multistep homology of the simplex and representations of symmetric groups
Published online by Cambridge University Press: 20 June 2019
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.
MSC classification
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 169 , Issue 2 , September 2020 , pp. 231 - 253
- Copyright
- © Cambridge Philosophical Society 2019