Module categories and subfactors from quantum groups

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• Hans Wenzl (University of California, San Diego)
• Thursday 29 June 2023, 14:10-14:50
• Seminar Room 1, Newton Institute.

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OASW05 - OAS Follow on: Operator Algebras: Subfactors and Applications

Let $V=\C^{$ be the vector representation of $SO(2N)$. We present $q$-deformations of End$(V}{\otimes n})$ which contain the centralizer of the action of the quantum group $U_q\so{2N}$ on $V^{\otimes n}$. This yields module categories of Rep $U_q\so_{2N}$. Our construction is inspired by our approach for type $A$ which, together with a recent construction by Copeland and Edie-Michell produces all non-exceptional module categories for fusion categories of Lie type $A$ (with the possible exception of some families for $SU(N)_k$ with $N$ odd, where some details still need to be worked out). In particular, our approach gives explicit information about the subfactors such as their indices and principal graphs in all those cases.

This talk is part of the Isaac Newton Institute Seminar Series series.

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