In this talk, we shall present a covariant generalization of the Stone-von Neumann Theorem to C*-dynamical systems that involve an action of a locally-compact Hausdorff abelian group G on the C*-algebra of compact operators on a Hilbert space. The main features of this generalization are (i) its representation of the Weyl Commutation Relation on a Hilbert C*-module, and (ii) its inclusion of two additional commutation relations (more precisely, covariance relations), which are needed to obtain a uniqueness theorem.
We shall also present an infinitesimal version of our result in the case where G is the group of reals, and discuss how this follows from new results in the theory of regular operators on Hilbert C*-modules as well as a powerful theorem by Jan Rusinek on the integrability of Lie-algebra representations.
Because of the Corona crisis, the lectures will be given as online lectures via zoom (or other video conference software). Please contact us by sending a message to our secretary Elke Enning, if you are interested to participate, so that we can send you an invitation for the lectures.