Representation theory seminar
Victor Protsak
UIC
Finite-dimensional representations of $\mathfrak{gl}(n)$
Abstract: We will review the basics of finite-dimensional representation theory of $\mathfrak{gl}(n)$, the general linear Lie algebra of $n\times n$ matrices. There are several well-known approaches to classification and explicit realization of representations: algebraic (highest weight theory and characters), algebro-geometric (flag varieties and standard monomials) and combinatorial (Gelfand-Tsetlin theory and Young tableaux). Perhaps less familiar is the noncommutative linear algebra aspect, rooted in the universal enveloping algebra and involving Capelli determinants and characteristic identities. Our goal is to present the theory and the tools for addressing the key questions of classification, construction and recognition of representations.
Watch out for possible room change
Tuesday September 18, 2018 at 4:00 PM in 512 SEO