Date of Award

1-1-2017

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School/Department

Department of Mathematics and Statistics

Content Description

1 online resource (ii, v, 51 pages)

Dissertation/Thesis Chair

Cristian Lenart

Committee Members

Antun Milas, Alexandre Tchernev, Changlong Zhong

Keywords

Affine algebraic groups, Representations of Lie algebras

Subject Categories

Physical Sciences and Mathematics

Abstract

KR crystals encode the structure of certain finite dimensional representations of affine Lie algebras. There are various combinatorial models for them; type specific ones, such as tableau models in classical types and type independent ones, such as the quantum alcove model. While the type specific models are more explicit, they have less easily accessible information, so it is generally hard to use them in specific computations. As these computations are much simpler in the quantum alcove model, an alternative is to translate them to the tableau models, via a crystal isomorphism between the two models. This was achieved in types A and C. The main goal of this thesis is to work towards generalizing these results to type B.

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