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Description

Given a fusion category C, the Brauer-Picard group BrPic(C) is the group of equivalence classes of invertible C-bimodule categories. It is an important invariant of C and appears as a key ingredient in group extensions of fusion categories. From a physics point of view, this group is also interesting, since it is the symmetry group of certain 3-dimensional topological quantum field theories. In this talk, I would like to present an approach to calculate the Brauer-Picard group of the representation category of a finite group by providing a natural decomposition.