Our recent approach to the Finkelberg-Kazhdan-Lusztig equivalence theorem centers on the construction of a fibre functor associated with the categories in the equivalence theorem, which in turn explains the underlying algebraic and analytic structure of the corresponding weak Hopf algebra in a new sense. We present a non-technical, historical perspective, a synthesis of the core arguments behind our proof, discuss these structural properties, and detail their applications to the rigidity and unitarizability of braided fusion categories arising from conformal field theory. We conclude by proposing open problems for future research.
The braided Doplicher-Roberts program and the Finkelberg-Kazhdan-Lusztig equivalence: A historical perspective, recent progress, and future directions / Pinzari, Claudia. - (2026). [10.48550/arXiv.2602.08348]
The braided Doplicher-Roberts program and the Finkelberg-Kazhdan-Lusztig equivalence: A historical perspective, recent progress, and future directions
Claudia Pinzari
2026
Abstract
Our recent approach to the Finkelberg-Kazhdan-Lusztig equivalence theorem centers on the construction of a fibre functor associated with the categories in the equivalence theorem, which in turn explains the underlying algebraic and analytic structure of the corresponding weak Hopf algebra in a new sense. We present a non-technical, historical perspective, a synthesis of the core arguments behind our proof, discuss these structural properties, and detail their applications to the rigidity and unitarizability of braided fusion categories arising from conformal field theory. We conclude by proposing open problems for future research.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
