Abstract
The original motivation for studying unitarizable representations of the braid group was to construct interesting examples of subfactors of II1 von Neumann factors. This is possible for representations factoring through Hecke algebras or q-Brauer algebras only if the deformation parameter is a root of unity. Information gained from this work can be applied to studying tensor products of representations of quantum groups at roots of unity and invariants of 3-manifolds.
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