## Quantum loop modules

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

## 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.## References

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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
- Received by editor(s): June 28, 2002
- Received by editor(s) in revised form: October 25, 2002
- Published electronically: February 26, 2003
- © Copyright 2003 American Mathematical Society
- Journal: Represent. Theory
**7**(2003), 56-80 - MSC (2000): Primary 17B67
- DOI: https://doi.org/10.1090/S1088-4165-03-00168-7
- MathSciNet review: 1973367

Dedicated: Dedicated to Anthony Joseph on the occasion of his 60th birthday