Document Type

Dissertation

Date of Degree

Summer 2013

Degree Name

PhD (Doctor of Philosophy)

Degree In

Mathematics

First Advisor

Julianna Tymoczko

Abstract

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.

Keywords

Algebra, Algebraic Geometry, Combinatorics, Representation Theory

Pages

ix, 120 pages

Bibliography

Includes bibliographical references (pages 118-120).

Copyright

Copyright 2013 Nicholas Teff

Included in

Mathematics Commons

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