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Commutative quantum current operators, semi-infinite construction and functional models


Authors: Jintai Ding and Boris Feigin
Journal: Represent. Theory 4 (2000), 330-341
MSC (2000): Primary 17B37
DOI: https://doi.org/10.1090/S1088-4165-00-00047-9
Published electronically: August 1, 2000
MathSciNet review: 1773865
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Abstract:

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.


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Additional Information

Jintai Ding
Affiliation: Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221-0025
Email: ding@math.uc.edu

Boris Feigin
Affiliation: Landau Institute of Theoretical Physics, Moscow, Russia

DOI: https://doi.org/10.1090/S1088-4165-00-00047-9
Received by editor(s): April 17, 1998
Received by editor(s) in revised form: January 14, 2000
Published electronically: August 1, 2000
Article copyright: © Copyright 2000 American Mathematical Society