Quantum loop modules

Details Quantum loop modules Quantum loop modules

2002-06-28

arxiv.org/abs/math/0206306v1

Represent. Theory 7 (2003), 56-80

Mathematics

Quantum Algebra

25 pages, AMSLaTeX

Scientific paper

10.1090/S1088-4165-03-00168-7

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 bases theory are discussed in a special case.

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