The paper reviews the construction of a fiber functor for the Finkelberg-Kazhdan-Lusztig equivalence and discusses its consequences for the structure of weak Hopf algebras and unitarizability of braided fusion categories from conformal field theory.
Kohno, Monodromy representations of braid groups and Yang-Baxter equations,Ann
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The braided Doplicher-Roberts program and the Finkelberg-Kazhdan-Lusztig equivalence: A historical perspective, recent progress, and future directions
The paper reviews the construction of a fiber functor for the Finkelberg-Kazhdan-Lusztig equivalence and discusses its consequences for the structure of weak Hopf algebras and unitarizability of braided fusion categories from conformal field theory.