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Representation Theory

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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
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

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
Article copyright: © Copyright 2000 American Mathematical Society