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 |
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Pages (from-to) | 1-23 |
Number of pages | 23 |
Journal | Mathematical Proceedings of the Cambridge Philosophical Society |
Early online date | 20 Jun 2019 |
DOIs | |
Publication status | E-pub ahead of print - 20 Jun 2019 |