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Quantum loop modules


Authors: Vyjayanthi Chari and Jacob Greenstein
Journal: Represent. Theory 7 (2003), 56-80
MSC (2000): Primary 17B67
DOI: https://doi.org/10.1090/S1088-4165-03-00168-7
Published electronically: February 26, 2003
MathSciNet review: 1973367
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Abstract: We classify the simple infinite-dimensional integrable modules with finite-dimensional weight spaces over the quantized enveloping algebra of an untwisted affine algebra. We prove that these are either highest (lowest) weight integrable modules or simple submodules of a loop module of a finite-dimensional simple integrable module and describe the latter class. Their characters and crystal basis theory are discussed in a special case.


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Additional Information

Vyjayanthi Chari
Affiliation: Department of Mathematics, University of California, Riverside, California 92521
Email: chari@math.ucr.edu

Jacob Greenstein
Affiliation: Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, 175 rue du Chevaleret, Plateau 7D, F-75013 Paris, France
Email: greenste@math.jussieu.fr

DOI: https://doi.org/10.1090/S1088-4165-03-00168-7
Received by editor(s): June 28, 2002
Received by editor(s) in revised form: October 25, 2002
Published electronically: February 26, 2003
Dedicated: Dedicated to Anthony Joseph on the occasion of his 60th birthday
Article copyright: © Copyright 2003 American Mathematical Society

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