Sur les caractères des groupes de Lie. (On the characters of Lie groups) (Q1822643)

Let G be a Lie group with Lie algebra \({\mathfrak g}\). Let \(\pi\) be a representation of G. The author studies the factor generated by \(\pi\) (G). The main result of the paper is the existence of operators of Hilbert-Schmidt class of the form \(\pi (u^ k*\phi)\) for \(\phi\in {\mathcal D}(G)\) and \(u\in \hat I\), where \(\hat I\) is the intersection of all the primitive ideals of U(\({\mathfrak g})\), containing the kernel I of the infinitesimal representation of U(\({\mathfrak g})\), corresponding to the representation \(\pi\). In the case of the normal factor representation \(\pi\) the author proves the existence of a trace class operator of the form \(\pi\) (\(\phi)\) for some \(\phi\in {\mathcal D}(G)\) relative to the factor generated by \(\pi\) (G).