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Quantum loop modules
Author(s):
Vyjayanthi
Chari;
Jacob
Greenstein
Journal:
Represent. Theory
7
(2003),
56-80.
MSC (2000):
Primary 17B67
Posted:
February 26, 2003
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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:
10.1090/S1088-4165-03-00168-7
PII:
S 1088-4165(03)00168-7
Received by editor(s):
June 28, 2002
Received by editor(s) in revised form:
October 25, 2002
Posted:
February 26, 2003
Dedicated:
Dedicated to Anthony Joseph on the occasion of his 60th birthday
Copyright of article:
Copyright
2003,
American Mathematical Society
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