Unitarizablity of premodular categories

Abstract

We study the unitarizability of premodular categories constructed from representations of quantum group at roots of unity. We introduce \emph{Grothendieck unitarizability} as a natural generalization of unitarizability to any class of premodular categories with a common Grothendieck semiring. We obtain new results for quantum groups of Lie types $F_4$ and $G_2$, and improve the known results for Lie types $B$ and $C$.

Version 2: proof of conjecture provided by referee, now Theorem 3.8 is sharp. To appear in J. Pure Appl. Algebra

References in corpus (3)

• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• From Quantum Groups to Unitary Modular Tensor Categories
• On a Family of Non-Unitarizable Ribbon Categories

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