Affinization of category O for quantum groups

@article{Young2012AffinizationOC,
  title={Affinization of category O for quantum groups},
  author={C. Young and E. Mukhin},
  journal={Transactions of the American Mathematical Society},
  year={2012},
  volume={366},
  pages={4815-4847}
}
  • C. Young, E. Mukhin
  • Published 2012
  • Mathematics
  • Transactions of the American Mathematical Society
  • 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… CONTINUE READING
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