Localization of unitary braid group representations

Understand

Governed by locality, we explore a connection between unitary braid group representations associated to a unitary $R$-matrix and to a simple object in a unitary braided fusion category.

• Unitary $R$-matrices, namely unitary solutions to the Yang-Baxter equation, afford explicitly local unitary representations of braid groups.
• Inspired by topological quantum computation, we study whether or not it is possible to reassemble the irreducible summands appearing in the unitary braid group representations from a unitary braided fusion category with possibly different positive multiplicities to get representations that are uniformly equivalent to the ones from a unitary R-matrix.
• Such an equivalence will be called a localization of the unitary braid group representations.