Homology Representations Arising from a Hypersimplex

Details Homology Representations Arising from a Hypersimplex Homology Representations Arising from a Hypersimplex

2011-08-30

arxiv.org/abs/1108.6001v1

Mathematics

Representation Theory

Scientific paper

We present a complete acyclic matching of the Hasse diagram associated with the face lattice of a hypersimplex. Since a hypersimplex is a convex polytope, there is a natural way to form a CW complex from its faces. We will then utilize this matching along with discrete Morse theory and some topological techniques to classify every subcomplex whose reduced homology groups are concentrated in a single degree. These reduced homology groups support a natural action of the symmetric group and a description of the characters that this action produces is given.

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