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Representation theory and reflection positivity

Karl-Hermann Neeb
Analysis Seminar
Thursday, 24 October, 2013, at 16:15, in Aud. D3 (1531-215)
Reflection positivity (sometimes called Osterwalder-Schrader positivity) was introduced by Osterwalder and Schrader in the context of axiomatic Quantum Field Theory. 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 describe a setup in which one can analyze more generally a correspondence between unitary representations of a Lie group with an involution and the Cartan dual Lie group (the euclidean motion group and the Poincare group are such a dual pair).
It turns out that the special case of one-parameter groups already provides a wealth of interesting structures that can be used in particular to understand reflection positivity for the ax+b-group and the Heisenberg group.
Contact person: Bent Ørsted