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arXiv · 1204.2769

Affinization of category O for quantum groups

C. A. S. Young·E. Mukhin
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Abstract

Let g be a simple Lie algebra. We consider the category O-hat of those modules over the affine quantum group Uq(g-hat) 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 O-hat. 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.

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C. A. S. Young, E. Mukhin. 2012-04-12. Affinization of category O for quantum groups. https://arxiv.org/abs/1204.2769

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