Quantum loop modules

Chari, Vyjayanthi; Greenstein, Jacob

doi:10.1090/S1088-4165-03-00168-7

Quantum loop modules
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by Vyjayanthi Chari and Jacob Greenstein

Represent. Theory 7 (2003), 56-80

DOI: https://doi.org/10.1090/S1088-4165-03-00168-7

Published electronically: 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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