Commutative quantum current operators, semiinfinite construction and functional models
Authors:
Jintai Ding and Boris Feigin
Journal:
Represent. Theory 4 (2000), 330341
MSC (2000):
Primary 17B37
DOI:
https://doi.org/10.1090/S1088416500000479
Published electronically:
August 1, 2000
MathSciNet review:
1773865
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Abstract  References  Similar Articles  Additional Information
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 semiinfinite 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 452210025
Email:
ding@math.uc.edu
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