Homology Representations Arising from a Hypersimplex
Representation Theory
2011-08-31 v1 Combinatorics
Geometric Topology
Abstract
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.
Cite
@article{arxiv.1108.6001,
title = {Homology Representations Arising from a Hypersimplex},
author = {Jacob T. Harper},
journal= {arXiv preprint arXiv:1108.6001},
year = {2011}
}