Remote Access Representation Theory
Green Open Access

Representation Theory

ISSN 1088-4165



Quantum loop modules

Authors: Vyjayanthi Chari and Jacob Greenstein
Journal: Represent. Theory 7 (2003), 56-80
MSC (2000): Primary 17B67
Published electronically: February 26, 2003
MathSciNet review: 1973367
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2000): 17B67

Retrieve articles in all journals with MSC (2000): 17B67

Additional Information

Vyjayanthi Chari
Affiliation: Department of Mathematics, University of California, Riverside, California 92521

Jacob Greenstein
Affiliation: Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, 175 rue du Chevaleret, Plateau 7D, F-75013 Paris, France

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