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.
Wenzl: Dualities for the spin representations, arXiv:2005.11299 [math.QA]
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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.