Affinization of category O for quantum groups

2012/04/12 by Charles A. S. Young, E. Mukhin, Young, C. A. S. +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1204.2769

openalex publication_date 2012/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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