Jordan algebras and generalized principal series representations
Let \(N\) be a semisimple Jordan algebra and let \(G\) be the group of conformal transformations of \(N\) and \(P\) the Poincaré group. We study certain induced representations of \(G\) from \(P\) and calculate the composition series in the compact picture. We find the Hermitian norm on each \(K\)-type. This generalizes recent results of \textit{K. D. Johnson} [Math. Ann. 287, 703-718 (1991; Zbl 0702.22017)] and of \textit{E. Kostant} and \textit{S. Sahi} [Adv. Math. 87, 71-92 (1991; Zbl 0748.22008)]. The author was informed by \textit{S. Sahi} that he has also obtained most of the above mentioned results in [Jordan algebras and degenerate principal series (to appear)].
generalized principal series representations
scientific article; zbMATH DE number 800588
scientific article