Two-parameter quantum vertex representations via finite groups and the McKay correspondence

Abstract

We introduce two-parameter quantum toroidal algebras of simply laced types and provide their group theoretic realization using finite subgroups of $S{L}_2(\mathbb{C})$ via McKay correspondence. In particular our construction contains a realization of the vertex representation of the two-parameter quantum affine algebras of $ADE$ types.

References in corpus (3)

• Drinfel'd Doubles and Lusztig's Symmetries of Two-Parameter Quantum Groups
• Representations of Two-parameter Quantum Orthogonal and Symplectic Groups
• Two-parameter Quantum Group of Exceptional Type G_2 and Lusztig's Symmetries