$U_q({\widehat{\mathfrak{gl}}}_{{}_N})$ action on ${\widehat{\mathfrak{gl}}}_{{}_N}$ -modules and quantum toroidal algebras

Abstract

We construct a vertex representation for the quantum toroidal algebra through the quantum general linear algebra. Using a new realization of the quantum general linear algebra we construct vertex operators for root vectors on the basic representation of the affine Lie algebra $g{l}_n$ and show that the simple generators give rise a realization of the quantum toroidal algebra with two parameters.

23 pages

References in corpus (2)

• Quantum vertex representations via finite groups and the McKay correspondence
• Representations of the Quantum Toroidal Algebra on highest weight modules of the Quantum Affine Algebra of type gl(N)

Cited by in corpus (9)

• The alternating presentation of $U_q(\widehat{g{l}_2})$ from Freidel-Maillet algebras
• On the second realization for the positive part of $U_q(\widehat{s{l}_2})$ of equitable type
• Quantum N-toroidal algebras and extended quantized GIM algebras of N-fold affinization
• A quantized Tits-Kantor-Koecher algebra
• Twisted quantum affinizations and quantization of extended affine Lie algebras
• A Twisted Quantum Toroidal Algebra
• Vertex representations of quantum N-toroidal algebras for type C
• Twisted quantum toroidal algebras $T_q^{-}(\mathfrak{g})$
• Level $-1/2$ realization of quantum N-toroidal algebras in type $C_n$