Journal of Lie Theory
Vol. 9, No. 1, pp. 157-191 (1999)

Desintegration des representations monomiales des groups de Lie nilpotents

A. Baklouti, J. Ludwig

Universite de Metz
Departement de Mathematiques
Ile du Saulcy, 57045 METZ Cedex 01

Abstract: Let $\scriptstyle G$ be a connected and simply connected nilpotent Lie group, let $\scriptstyle H$ be a closed connected subgroup of $\scriptstyle G$ and let $\scriptstyle \chi$ be a unitary character of {$\scriptstyle H$}. We construct explicitly a smooth intertwining operator between the monomial representation $ \scriptstyle \pi = \hbox{ind}_H^G\chi$ of $\scriptstyle G$ and its decomposition into irreducibles. In particuliar, we present a new disintegration of $\scriptstyle L^2(G)$.

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