Unitarizablity of premodular categories
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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 $C$.