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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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Quantum loop modules
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by Vyjayanthi Chari and Jacob Greenstein PDF
Represent. Theory 7 (2003), 56-80 Request permission


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:
  • Jacob Greenstein
  • Affiliation: Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, 175 rue du Chevaleret, Plateau 7D, F-75013 Paris, France
  • Email:
  • 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
  • © Copyright 2003 American Mathematical Society
  • Journal: Represent. Theory 7 (2003), 56-80
  • MSC (2000): Primary 17B67
  • DOI:
  • MathSciNet review: 1973367