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September 4, 2020

Representations of rigid C*-tensor categories over GJS C*-algebras

We will construct a fully faithful bi-involutive strong monoidal representation of an arbitrary countably generated RC*TC onto a subcategory of finitely generated projective Hilbert C*-bimodules over a simple separable unital monotracial C*-algebra, using the diagrammatic methods from Guionnet, Jones and Shlyakhtenko. Out of this category of bimodules we will construct a similar functor into the bifinite and spherical bimodules over an interpolated free group factor. The composite of these two functors recovers the representation constructed by Brothier, Hartglass and Penneys. Based on joint work with Hartglass arXiv:2005.09821.