We apply the concept of reflection positivity in euclidean quantum field theory to the complementary series of S_SL_(2_n_, 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(2_n_, ℂ. The possible relation to the theory of noncommuting monodromy matrices appearing in the theory of integrable quantum systems is briefly discussed.
Cite this article
Robert Schrader, Reflection Positivity for the Complementary Series of <i>SL</i>(2<i>n</i>, <i>ℂ</i>). Publ. Res. Inst. Math. Sci. 22 (1986), no. 1, pp. 119–141DOI 10.2977/PRIMS/1195178376