Representation theory of a Quantum SU(2)


Ryan Seelig


UNSW Sydney


Fri, 16/04/2021 - 1:00pm


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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. 

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