CU Algebraic Lie Theory Seminar

Schur-Weyl Duality

Richard Green, CU

Abstract

We will introduce the Serre presentation of the enveloping algebra associated to a Lie algebra, and use it to construct the r-fold tensor power of the natural representation of the Lie algebra of gl_n. This provides the framework in which to discuss Schur-Weyl duality and Schur algebras. We will present a result of Doty and Giaquinto explaining how to extend the Serre presentation to a presentation of the Schur algebra S(n, r).