# 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 $$\mathfrak{gl}_\infty$$.