Representations of the Quantum Toroidal Algebra on Highest Weight Modules of the Quantum Affine Algebra of Type <strong>gl</strong><sub><em>N</em></sub>
Kouichi Takemura
Kyoto University, JapanDenis Uglov
Kyoto University, Japan

Abstract
A representation of the quantum toroidal algebra of type slN is defined on every integrable irreducible highest weight module of the quantum affme algebra of type glN. The q-version of the level-rank duality giving the reciprocal decomposition of the q-Fock space with respect to mutually commutative actions of U'q(glN) of level L and U'g(slL) of level N is described.
Cite this article
Kouichi Takemura, Denis Uglov, Representations of the Quantum Toroidal Algebra on Highest Weight Modules of the Quantum Affine Algebra of Type <strong>gl</strong><sub><em>N</em></sub>. Publ. Res. Inst. Math. Sci. 35 (1999), no. 3, pp. 407–450
DOI 10.2977/PRIMS/1195143609