Some quotient algebras arising from the quantum toroidal algebra $U_{q}(sl_2(\mathcal{C}_{\gamma}))$

Abstract

Some quotient algebras arising from the quantum toroidal algebra $U_{q}(\mathit{sl}_{2}(\mathcal{C}_{\gamma}))$ are considered. They are related to integrable highest weight representations of the algebra and are shown to be isomorphic to direct sums of tensor products of two algebras of symmetric Laurent polynomials and Macdonald's difference operators.