Analytic continuation of Flensted-Jensen representations (Q1191462)

In earlier papers the authors found explicit formulas for Flensted-Jensen functions corresponding to scalar holomorphic discrete series representations of \(G\). This led to intertwining operators between holomorphic vector bundles on \(G/K\) and functions on \(G/H\) as well as a multiplicity one result for these representations on \(G/H\). Here they extend these results to modules obtained by analytic continuation in the defining parameters. They obtain, for example, an alternative way of computing the Wallach set [\textit{N. Wallach}, Trans. Am. Math. Soc. 251, 1-17 and 19-37 (1979; Zbl 0419.22017 and Zbl 0419.22018)].