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

Jing, Naihuan; Zhang, Honglian

doi:10.1090/S0002-9947-2011-05284-0

Two-parameter quantum vertex representations via finite groups and the McKay correspondence
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Trans. Amer. Math. Soc. 363 (2011), 3769-3797 Request permission

Abstract:

We provide a group-theoretic realization of two-parameter quantum toroidal algebras using finite subgroups of $SL_2(\mathbb C)$ via McKay correspondence. In particular our construction contains the vertex representation of the two-parameter quantum affine algebras of $ADE$ types as special subalgebras.

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