Coideal algebras and subfactors

It is well-known that certain classes of coideal algebras of Drinfeld-Jimbo quantum groups can be used to construct analogs of symmetric spaces in the quantum setting. We study the question whether such constructions also exist if the deformation parameter is a root of unity, at the level of so-called fusion tensor categories. We can answer this affirmatively for the important special cases of analogs of embeddings of SO(N) resp. Sp(N) into SU(N). The resulting subfactors can be viewed as finite approximations of the embeddings of these Lie groups in the framework of module tensor categories. This will be made precise in the talk.