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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Two-parameter quantum vertex representations via finite groups and the McKay correspondence
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by Naihuan Jing and Honglian Zhang PDF
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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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