This talk will be split into two parts. In the first part I will describe a hypersimplex and go over concepts of Coxeter groups and topology in order to get a better understanding of this polytope. In the second talk I will describe a matching on the face lattice of a hypersimplex and use discrete Morse theory to classify all subcomplexes whose reduced homology groups are concentrated in a single degree. These homology groups support a natural action of the symmetric group and I will finish my talk by describing the characters that this action produces.
Homology representations arising from a hypersimplex II
Homology representations arising from a hypersimplex II