8 Nov 2013; IMS (UiTø), room U1=A228. 13:00-14:00.

Hilja Huru (UiT), joint with Valentin Lychagin

“Quantization of representations of compact connected Lie groups and applications to Hilbert-Schmidt operators”

We investigate quantizations in the monoidal categories of unitary representations of compact connected Lie groups.

For the n-dimensional torus T we show that the set of quantizations is isomorphic to the N-dimensional torus, where N=n(n-1)/2. For connected compact Lie groups G of rank n, we get the result that the set of quantizations of G is isomorphic to the set of quantizations of its maximal torus T invariant under action by its Weyl group.

We apply the result to find quantizations of the action of Hilbert-Schmidt operators.