Representations of the Quantum Toroidal Algebra on highest weight modules of the Quantum Affine Algebra of type gl(N)

Abstract

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

References in corpus (2)

• Schur duality in the toroidal setting
• Level-0 structure of level-1 $U_q({\widehat{sl}}_2)$-modules and Macdonald polynomials

Cited by in corpus (5)

• Toroidal and level 0 U'_q(\hat{sl_{n+1}}) actions on U_q(\hat{gl_{n+1}}) modules
• Quantum affine Gelfand-Tsetlin bases and quantum toroidal algebra via K-theory of affine Laumon spaces
• $U_q({\widehat{\mathfrak{gl}}}_{{}_N})$ action on ${\widehat{\mathfrak{gl}}}_{{}_N}$ -modules and quantum toroidal algebras
• On Guay's evaluation map for affine Yangians
• Canonical bases of higher-level q-deformed Fock spaces