Emmy-Noether-Seminar

The monoidal center of Deligne’s interpolation category Rep(S_t)

Johannes Flake (Aachen)

Abstract: The representations of the symmetric group on n letters form a semisimple tensor category for each natural number n. Pierre Deligne defined a family of monoidal categories parametrized by the complex numbers which interpolate those categories in a certain precise sense. I will explain this construction and discuss joint work with Robert Laugwitz about the monoidal center of Deligne’s categories yielding, in particular, interpolation objects for Yetter–Drinfeld modules of the symmetric group and link invariants which interpolate Dijkgraaf–Witten invariants.