University of Sydney Algebra Seminar

Natasha Rozhkovskaya (Kansas State University)

Friday 20 May, 12:05-12:55pm, Carslaw 175

The \(q\)-characters of representations of quantum affine algebras

The \(q\)-characters of a quantum affine algebra are combinatorial objects that describe the structure of irreducible finite-dimensional representations of this algebra. The evaluation map allows to use the \(q\)-characters of quantum affine algebra of type \(A_n\) as a combinatorial tool for description of the underlying Lie algebra \(\mathfrak{sl}_n\) or \(\mathfrak{gl}_n\). In the talk we will illustrate this application on corresponding examples and compute \(q\)-characters of certain class of modules of quantum affine algebra of \(\mathfrak{gl}_\infty\).