Topologically irreducible representations of the Schwartz-algebra of a nilpotent Lie group
Let N be a connected, simply connected nilpotent Lie group and let S(N) be its Schwartz-algebra. Let E be a locally convex topological vector space and let T be a continuous topologically irreducible representation of S(N) on E. We show that the restriction of T to the subspace \(E^{\infty}=T(S(N))E\) of E is algebraically irreducible and that the kernel ker T of T is of the form ker \(\pi\), where \(\pi\) is an irreducible unitary representation of S(N). We extend thus to general spaces E, using a new proof, the results of \textit{F. Du Cloux} [Représentations tempérées des groupes de Lie nilpotents (Preprint 1987)], who treated the case of Fréchet spaces E.
scientific article; zbMATH DE number 4086265
scientific article