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.
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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. 407–450DOI 10.2977/PRIMS/1195143609