XXXIII Workshop on Geometric Methods in Physics 29.06-5.07.2014

Karl-Hermann Neeb

A representation theoretic perspective on reflection positivity

Reflection positivity (sometimes called Osterwalder-Schrader positivity) was introduced by Osterwalder and Schrader in the context of axiomatic euclidean field theories. On the level of unitary representations, it provides a passage from representations of the euclidean isometry group to representations of the Poincaré group. In our talk we shall explain how these ideas can be used to obtain a natural context for the passage from representations of symmetric Lie groups to representations of their dual Lie group. In particular, we shall discuss the role of distribution vectors and reproducing kernels in this picture and how distributions on a Lie group can lead to “reflection positive“ representations.

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