Braid representations from quantum groups of exceptional Lie type

Abstract

We study the problem of determining if the braid group representations obtained from quantum groups of types $E,F$ and $G$ at roots of unity have infinite image or not. In particular we show that when the fusion categories associated with these quantum groups are not weakly integral, the braid group images are infinite. This provides further evidence for a recent conjecture that weak integrality is necessary and sufficient for the braid group representations associated with any braided fusion category to have finite image.

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Cited by in corpus (5)

• $SO(N{)}_2$ Braid group representations are Gaussian
• Low-dimensional representations of the three component loop braid group
• Braid Representations from Unitary Braided Vector Spaces
• Local unitary representations of the braid group and their applications to quantum computing
• Generalized and quasi-localizations of braid group representations