Quantum loop algebras and l-root operators

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    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.
    Original languageEnglish
    Pages (from-to)1195-1226
    Number of pages32
    JournalTransformation Groups
    Issue number4
    Early online date18 Sept 2015
    Publication statusPublished - 1 Dec 2015


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