University of Hertfordshire

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Quantum loop algebras and l-root operators

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Original languageEnglish
Number of pages32
Pages (from-to)1195-1226
JournalTransformation Groups
Journal publication date1 Dec 2015
Volume20
Issue4
Early online date18 Sep 2015
DOIs
Publication statusPublished - 1 Dec 2015

Abstract

Let g be a simple Lie algebra and q transcendental. We consider the category C_P of finite-dimensional representations of the quantum loop algebra Uq(Lg) in which the poles of all l-weights belong to specified finite sets P. Given the data (g,q,P), we define an algebra A whose raising/lowering operators are constructed to act with definite l-weight (unlike those of Uq(Lg) itself). It is shown that there is a homomorphism Uq(Lg) -> A such that every representation V in C_P is the pull-back of a representation of A.

Notes

This is the accepted manuscript of the following article: Charles Young, “Quantum loop algebras and l-root operators”, Transformation Groups, Vol. 20(4): 1195-1226, September 2015. The final published version is available at: https://link.springer.com/article/10.1007%2Fs00031-015-9339-4 © Springer Science+Business Media New York (2015)

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