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GENERALIZED AND QUASILOCALIZATIONS OF BRAID GROUP REPRESENTATIONS
"... We develop a theory of localization for braid group representations associated with objects in braided fusion categories and, more generally, to YangBaxter operators in monoidal categories. The essential problem is to determine when a family of braid representations can be uniformly modelled upon a ..."
Abstract

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We develop a theory of localization for braid group representations associated with objects in braided fusion categories and, more generally, to YangBaxter operators in monoidal categories. The essential problem is to determine when a family of braid representations can be uniformly modelled upon a tensor power of a fixed vector space in such a way that the braid group generators act “locally”. Although related to the notion of (quasi)fiber functors for fusion categories, remarkably, such localizations can exist for representations associated with objects of nonintegral dimension. We conjecture that such localizations exist precisely when the object in question has dimension the squareroot of an integer and prove several key special cases of the conjecture.
Quantum Fourier Transforms and the Complexity of Link Invariants for Quantum Doubles of Finite Groups
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SO(N)2 Braid group representations are Gaussian
 in preparation. BRAID REPRESENTATIONS FROM UNITARY BRAIDED VECTOR SPACES 17
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