UNITARY BRAID REPRESENTATIONS

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.