Two-parameter quantum vertex representations via finite groups and the McKay correspondence
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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.References
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Additional Information
- Naihuan Jing
- Affiliation: School of Sciences, South China University of Technology, Guangzhou 510640, People’s Republic of China – and – Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695
- MR Author ID: 232836
- Email: jing@math.ncsu.edu
- Honglian Zhang
- Affiliation: Department of Mathematics, Shanghai University, Shanghai 200444, People’s Republic of China
- Email: hlzhangmath@shu.edu.cn
- Received by editor(s): September 9, 2009
- Received by editor(s) in revised form: December 15, 2009
- Published electronically: February 16, 2011
- Additional Notes: The second author was the corresponding author for this paper.
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 363 (2011), 3769-3797
- MSC (2000): Primary 17B20
- DOI: https://doi.org/10.1090/S0002-9947-2011-05284-0
- MathSciNet review: 2775827