## 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.

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 language | English |
---|---|

Pages (from-to) | 4815-4847 |

Journal | Transactions of the American Mathematical Society |

Volume | 366 |

Early online date | 5 May 2014 |

DOIs | |

Publication status | Published - 2014 |

## Keywords

- Quantum Affine Algebras
- Representation Theory
- Quantum Groups