Jacobsen, Jacob; Stetkaer, Henrik Ultra-irreducibility of induced representations. (English) Zbl 0706.22004 Math. Scand. 68, No. 2, 305-318 (1991). We prove irreducibility criteria for representations of Lie groups induced from finite dimensional representations of closed subgroups. The representations need not be unitary and the setup allows the representation spaces of the induced representations to be chosen among a variety of different function and distribution spaces. The notion of irreducibility considered is that of ultra-irreducibility which is stronger than complete and topological irreducibility. The criteria are applied to semi-direct products and to nilpotent groups. Reviewer: J.Jacobsen MSC: 22D30 Induced representations for locally compact groups 22E27 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.) Keywords:irreducibility criteria; representations of Lie groups; induced representations; ultra-irreducibility; semi-direct products; nilpotent groups PDFBibTeX XMLCite \textit{J. Jacobsen} and \textit{H. Stetkaer}, Math. Scand. 68, No. 2, 305--318 (1991; Zbl 0706.22004) Full Text: DOI EuDML