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


Authors: Naihuan Jing and Honglian Zhang
Journal: Trans. Amer. Math. Soc. 363 (2011), 3769-3797
MSC (2000): Primary 17B20
DOI: https://doi.org/10.1090/S0002-9947-2011-05284-0
Published electronically: February 16, 2011
MathSciNet review: 2775827
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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.


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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
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

DOI: https://doi.org/10.1090/S0002-9947-2011-05284-0
Keywords: Two-parameter quantum affine algebra, finite groups, wreath products, McKay correspondence.
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.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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