Publications of the Research Institute for Mathematical Sciences
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Reflection Positivity for the Complementary Series of SL(2n, ℂ)
Robert Schrader (1)(1) Institut für theoretische Physik, Freie Universität Berlin, Arnimallee 2-6, 14195, BERLIN, GERMANY
We apply the concept of reflection positivity in euclidean quantum field theory to the complementary series of SSL(2n, ℂ as given by Gelfand and Neumark for n=1 and by Stein for n>1. The result is a virtual representation in the sense of Fröhlich, Osterwalder and Seiler or equivalently a strongly continuous representation of a closed subsemigroup by contractions on a new Hilbert space. Analytic continuation gives a unitary representation of a certain dual group of SL(2n, ℂ. The possible relation to the theory of noncommuting monodromy matrices appearing in the theory of integrable quantum systems is briefly discussed.
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