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Journal of Lie Theory 24 (2014), No. 3, 865--887
Copyright Heldermann Verlag 2014

Restrictions des séries discrètes de certains groupes résolubles

Sami Kouki
Département de Mathématiques, Faculté des Sciences de Tunis, Campus Universitaire, 1060 Tunis, Tunisia


The study of restrictions of unitary irreducible representations of a Lie group $G$ to its closed subgroups was successfully made by Corwin-Greenleaf for the nilpotent case, Lipsman for the completely solvable case and Fujiwara for the exponential case. However, even if the orbit method describes a large set of representations in $\widehat G$, the study of these restrictions remains a very difficult problem in the general case. In this work, we study the restriction of square integrable representations modulo the center of a solvable connected group, semi-direct product of a torus by a Heisenberg group to its algebraic connected subgroups.

Keywords: Discrete series, representations, restriction, multiplicities.

MSC: 06B15

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