Speaker: **Makoto Yamashita** (Ochanomizu University)

Title: Drinfeld center and representation theory for monoidal categories

Time/Date: 4:45-6:15pm, Wednesday, December 2, 2015

Room: 118 Math. Sci. Building

Abstract:
Given a rigid C^{*}-tensor category C and a unitary half-braiding on an
ind-object, we construct a *-representation of the fusion algebra of C.
This is motivated by the relation between the Drinfeld double and
central property (T) for quantum groups, and it turns out to be
equivalent to the notion of admissible representation considered by
Popa and Vaes. When C is realized by Hilbert bimodules over a II_{1}-factor,
the Drinfeld center can be presented as a category of Hilbert bimodules
over another II_{1}-factor obtained by the Longo-Rehren construction. We
also study Müger's notion of weakly monoidal Morita equivalence, and
analyze the behavior of our constructions under the equivalence of the
corresponding Drinfeld centers established by Schauenburg. In particular,
we prove that property (T) is invariant under such relation. Based on
joint work with S. Neshveyev (arXiv:1501.07390).