On the decomposition of tensor products of principal series representations for real-rank one semisimple groups

Martin, Robert Paul

doi:10.1090/S0002-9947-1975-0374341-0

On the decomposition of tensor products of principal series representations for real-rank one semisimple groups
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Trans. Amer. Math. Soc. 201 (1975), 177-211 Request permission

Abstract:

Let $G$ be a connected semisimple real-rank one Lie group with finite center. It is shown that the decomposition of the tensor product of two representations from the principal series of $G$ consists of two pieces, ${T_c}$ and ${T_d}$, where ${T_c}$ is a continuous direct sum with respect to Plancherel measure on $\hat G$ of representations from the principal series only, occurring with explicitly determined multiplicities, and ${T_d}$ is a discrete sum of representations from the discrete series of $G$, occurring with multiplicities which are, for the present, undetermined.

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