Let G' ⊂ G be real reductive Lie groups. This paper offers a criterion on the triplet (G, G', π) that the irreducible unitary representation π of G splits into a discrete sum of irreducible unitary representations of a subgroup G' when restricted to G', each of finite multiplicity. Furthermore, we shall give an upper estimate of the multiplicity of an irreducible unitary representation of G' occurring in π|G'.
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© Toshiyuki Kobayashi