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Module categories and subfactors from quantum groups

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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.

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