Geodesic
Restricting Representations of Completely Solvable Lie Groups
Canadian journal of mathematics, Tome 42 (1990) no. 5, pp. 790-824

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We are concerned here with the problem of describing the direct integral decomposition of a unitary representation obtained by restriction from a larger group. This is the dual problem to the more commonly investigated problem of decomposing induced representations. In this paper we work in the context of completely solvable Lie groups—more general than nilpotent, but less general than exponential solvable. Moreover, the groups involved are simply connected. The restriction problem was considered originally in [2] and in [6] for nilpotent groups. 
Lipsman, R. L. Restricting Representations of Completely Solvable Lie Groups. Canadian journal of mathematics, Tome 42 (1990) no. 5, pp. 790-824. doi: 10.4153/CJM-1990-042-9
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