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Representation Theory

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

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Commutative quantum current operators, semi-infinite construction and functional models
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by Jintai Ding and Boris Feigin PDF
Represent. Theory 4 (2000), 330-341 Request permission


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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Additional 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