Representation theory of a Quantum SU(2)

Abstract:

To avoid paradoxes, the geometry of physics at the very smallest scales must be non-commutative. The symmetries of such a geometry constitute a structure called a Quantum Group. In this talk we build one instance of a quantum group - quantum SU(2), and study its representation theory. This theory leads us to a beautiful generalisation of Pontryagin duality - Tannaka-Krein duality for compact quantum groups, which says that any C*-tensor category with a fibre functor can be realised as the representation category of some compact quantum group up to a natural equivalence.