Representations of the Quantum Toroidal Algebra on highest weight modules of the Quantum Affine Algebra of type gl(N)
Abstract
Description
A representation of the Quantum Toroidal Algebra of type sl(N) is constructed on every irreducible integrable highest weight module of the Quantum Affine Algebra of type gl(N). As an intermediate step in the construction, we obtain a quantum analogue of the classical level-rank duality, describing the reciprocal decomposition of the q-Fock space with respect to mutually commutative actions of U_q(gl(N)^) of level L, and U_q(sl(L)^) of level N.
LaTeX 2e, 35 pages
LaTeX 2e, 35 pages