Abstract
The irreducible representations of the noncompact groups SO(n,1) and U(n,1) are discussed in the space of functions on the compact groups SO(n) and U(n), and then it is shown that the Hermitian form scalar product with a nonintertwining operator can be introduced for each of the complementary and the discrete series of the unitary irreducible representations (UIR) of the groups SO(n,1) and U(n,1). The positive definite scalar product can be introduced for all classes except for a discrete series in the case of U(n,1).
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