Date of Award
8-1-2016
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.
Recommended Citation
Lhou, Hassan, "Restricting a Representation to a Principally Embedded Sl(2) Subalgebra" (2016). Theses and Dissertations. 1290.
https://dc.uwm.edu/etd/1290