Date of Degree
PhD (Doctor of Philosophy)
The Hessenberg representation is a representation of the symmetric group afforded on the cohomology ring of a regular semisimple Hessenberg variety. We study this representation via a combinatorial presentation called GKM Theory. This presentation allows for the study of the representation entirely from a graph.
The thesis derives a combinatorial construction of a basis of the equivariant cohomology as a free module over a polynomial ring. This generalizes classical constructions of Schubert classes and divided difference operators for the equivariant cohomology of the flag variety.
Algebra, Algebraic Geometry, Combinatorics, Representation Theory
ix, 120 pages
Includes bibliographical references (pages 118-120).
Copyright 2013 Nicholas Teff