Restricting a Representation to a Principally Embedded Sl(2) 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.