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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Tensor products of principal series for the De Sitter group


Author: Robert P. Martin
Journal: Trans. Amer. Math. Soc. 265 (1981), 121-135
MSC: Primary 22E43; Secondary 22E45, 81C40
MathSciNet review: 607111
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Abstract: The decomposition of the tensor product of two principal series representations is determined for the simply connected double covering, $ G = {\text{Spin}}(4,1)$, of the DeSitter group. The main result is that this decomposition 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 and $ {T_d}$ is a discrete sum of representations from the discrete series of $ G$. The multiplicities of representations occurring in $ {T_c}$ and $ {T_d}$ are all finite.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1981-0607111-9
PII: S 0002-9947(1981)0607111-9
Article copyright: © Copyright 1981 American Mathematical Society