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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Commutative quantum current operators, semi-infinite construction and functional models
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by Jintai Ding and Boris Feigin
Represent. Theory 4 (2000), 330-341
Published electronically: August 1, 2000


We construct the commutative current operator $\bar x^+(z)$ inside $U_q(\hat {\mathfrak {sl}}(2))$. With this operator and the condition of quantum integrability on the quantum currents of $U_q(\hat {\mathfrak {sl}}(2))$, we derive the quantization of the semi-infinite construction of integrable modules of $\hat {\mathfrak {sl}}(2)$ which has been previously obtained by means of the current operator $e(z)$ of $\hat {\mathfrak {sl}}(2)$. The quantization of the functional models for $\hat {\mathfrak {sl}}(2)$ is also given.
    [DM] DM J. Ding and T. Miwa Zeros and poles of quantum current operators and the condition of quantum integrability, q-alg/9608001,RIMS-1092. [DI] DI J. Ding and K. Iohara Generalization and deformation of the quantum affine algebras, Rims-1090, q-alg/9608002.
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Bibliographic Information
  • Jintai Ding
  • Affiliation: Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221-0025
  • Email:
  • Boris Feigin
  • Affiliation: Landau Institute of Theoretical Physics, Moscow, Russia
  • Received by editor(s): April 17, 1998
  • Received by editor(s) in revised form: January 14, 2000
  • Published electronically: August 1, 2000
  • © Copyright 2000 American Mathematical Society
  • Journal: Represent. Theory 4 (2000), 330-341
  • MSC (2000): Primary 17B37
  • DOI:
  • MathSciNet review: 1773865