Reflection positivity for the complementary series of SL(2n, \({\mathbb{C}})\) (Q1080963)

The concept of reflection positivity is defined in the context of unitary representations of groups and is applied to the complementary series of SL(2n, \({\mathbb{C}})\). It gives rise to a local representation of SL(2n, \({\mathbb{C}})\) in the sense of Jorgensen or \textit{J. Fröhlich}, \textit{K. Osterwalder} and \textit{E. Seiler} [Ann. Math., II. Ser. 118, 461-489 (1983; Zbl 0537.22017)]. Analytic continuation gives a unitary representation of a dual group of SL(2n, \({\mathbb{C}}).\) These results provide with some insight into the group theoretical understanding of Yang-Baxter equations.