Finite dimensional representations of quantum affine algebras

Supervisor

Prof. Peter Bouwknegt Phone: 6125 2969

Quantum affine algebras are deformations of affine Lie algebras (central extensions of loop algebras). Understanding their representation theory is of utmost importance in the study of, e.g., integrable models of statistical mechanics. As yet, however, even the finite dimensional irreducible representations are poorly understood except in the simplest cases. The aim of this project is to formulate a conjecture on the general structure of finite dimensional irreducible representations of quantum affine algebras consistent with what is known already.