# The q-characters of representations of quantum affine algebras

Algebra/Geometry/Topology Seminar

#### by Natalia Rozhkovskaya

Institution: Kansas State University, Kansas, USA
Date: Thu 16th June 2011
Time: 3:15 PM
Location: Room 215, Richard Berry Building, The University of Melbourne

Abstract: 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 $$sl_n$$ or $$gl_n$$. 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 $$gl_\infty$$ .