an:04150534
Zbl 0702.22012
Fujiwara, Hidenori
Sur les restrictions des repr??sentations unitaires des groupes de Lie r??solubles exponentiels. (On the restrictions of unitary representations of exponential solvable Lie groups)
FR
Invent. Math. 104, No. 3, 647-654 (1991).
00157096
1991
j
22E27
exponential solvable Lie group; central decomposition; orbit method; Frobenius reciprocity; tensor product of unitary representations
Let G be an exponential solvable Lie group, \(\pi\) an irreducible unitary representation of G, and let K be an analytic subgroup of G. We describe the canonical central decomposition of the restriction of \(\pi\) to K. This is done by the orbit method due to Kirillov. As corollary, we observe a Frobenius reciprocity and get the irreducible decomposition of the tensor product of unitary representations. These results were first shown by Corwin and Greenleaf in nilpotent case, then by Lipsman in completely solvable case.
H.Fujiwara