Degree Type

Thesis

Date of Award

2020

Degree Name

Doctor of Philosophy

Department

Mathematics

Major

Mathematics

First Advisor

Jonas T Hartwig

Abstract

We begin by presenting the crystal structure of finite-dimensional irreducible representations of the special linear Lie algebra in terms of Gelfand-Zeitlin patterns. We then define a crystal structure using the set of symplectic Zhelobenko patterns, parametrizing bases for finite-dimensional irreducible representations of sp4. This is obtained by a bijection with Kashiwara-Nakashima tableaux and the symplectic jeu de taquin of Sheats and Lecouvey. We offer some conjectures on the generalization of this structure to rank n as well as a bijection and crystal structure in certain special cases.

DOI

https://doi.org/10.31274/etd-20200624-214

Copyright Owner

O'Neill Kingston

Language

en

File Format

application/pdf

File Size

67 pages

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