Affinization of category O for quantum groups

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.

arXiv comment32 pages, latex

References in corpus (3)

• New features of FORM
• Asymptotic representations and Drinfeld rational fractions
• Path description of type B q-characters

Cited by in corpus (10)

• Oscillator versus prefundamental representations II. Arbitrary higher ranks
• Oscillator versus prefundamental representations
• Graded Limits of Minimal Affinizations in Type D
• Asymptotic Representations of Quantum Affine Superalgebras
• M-systems and Cluster algebras
• Length-two representations of quantum affine superalgebras and Baxter operators
• Quantum groups and functional relations for arbitrary rank
• On the extended T-system of type $C_3$
• Unipotent quantum coordinate ring and prefundamental representations for types $A_n^{(1)}$ and $D_n^{(1)}$
• Quantum loop algebras and l-root operators