Affinization of category O for quantum groups

C. A. S. Young, E. Mukhin

Research output: Working paperPreprint


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.
Original languageEnglish
Number of pages32
Publication statusUnpublished - 12 Apr 2012

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