Representations of the Quantum Toroidal Algebra on Highest Weight Modules of the Quantum Affine Algebra of Type

  • Kouichi Takemura

    Kyoto University, Japan
  • Denis Uglov

    Kyoto University, Japan

Abstract

A representation of the quantum toroidal algebra of type is defined on every integrable irreducible highest weight module of the quantum affme algebra of type . The -version of the level-rank duality giving the reciprocal decomposition of the -Fock space with respect to mutually commutative actions of of level and of level 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 . Publ. Res. Inst. Math. Sci. 35 (1999), no. 3, pp. 407–450

DOI 10.2977/PRIMS/1195143609