Affinization of category O for quantum groups

Charles A. S. Young, Evgeny Mukhin

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    14 Citations (Scopus)
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    Abstract

    Let g be a simple Lie algebra. We consider the category ˆO of those modules over
    the affine quantum group Uq(bg) whose Uq(g)-weights have finite multiplicity and lie in a finite union of cones generated by negative roots. We show that many properties of the category of the finite-dimensional representations naturally extend to the category ˆO . In particular, we develop the theory of q-characters and define the minimal affinizations of parabolic Verma modules. In types ABCFG we classify these minimal affinizations and conjecture a Weyl denominator type formula
    for their characters.
    Original languageEnglish
    Pages (from-to)4815-4847
    JournalTransactions of the American Mathematical Society
    Volume366
    Early online date5 May 2014
    DOIs
    Publication statusPublished - 2014

    Keywords

    • Quantum Affine Algebras
    • Representation Theory
    • Quantum Groups

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