Date of Award

August 2016

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Jeb F. Willenbring

Committee Members

Jeb Willenbring, Craig Guilbault, Istvan Lauko, Ian Musson, Hans Volkmer

Keywords

Branching Algebra, Cartan-Helgason Theorem, Hermite Reciprocity, Pieri Rules, Small Lie Subalgebra

Abstract

Fix n>2. Let s be a principally embedded sl(2)-subalgebra in sl(n). A special case of work by Jeb Willenbring and Gregg Zuckerman implies that there exists a positive integer b(n) such that for any finite dimensional sl(n)-representation, V, there exists an irreducible s-representation embedding in V with dimension at most b(n). We prove that the best possible value for the bound is b(n)=n.

Included in

Mathematics Commons

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