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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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


Author: Robert Paul Martin
Journal: Trans. Amer. Math. Soc. 201 (1975), 177-211
MSC: Primary 22E45
DOI: https://doi.org/10.1090/S0002-9947-1975-0374341-0
MathSciNet review: 0374341
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1975-0374341-0
Keywords: Semisimple Lie groups, irreducible unitary representations, cuspidal parabolic subgroups, principal series, discrete series, tensor products
Article copyright: © Copyright 1975 American Mathematical Society