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Transactions of the American Mathematical Society

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



Tensor products for $\textrm {SL}(2, k)$

Author: Robert P. Martin
Journal: Trans. Amer. Math. Soc. 239 (1978), 197-211
MSC: Primary 22E45; Secondary 22E50
MathSciNet review: 487045
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Abstract: Let G be ${\text {SL}}(2,k)$ where k is a locally compact, nondiscrete, totally disconnected topological field whose residual characteristic is not 2, ${\pi _\sigma }$, be a principal series representation of G, and $\pi \in \hat G$ be arbitrary. We determine the decomposition of ${\pi _\sigma } \otimes \pi$ into irreducibles by reducing this problem to decomposing the restriction of each $T \in \hat G$ to a minimal parabolic subgroup B of G and decomposing certain tensor products of irreducibles of B.

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Keywords: Local field, tensor product, irreducible unitary representation, principal series, supplementary series, discrete series, the special representation, Plancherel measure, minimal parabolic subgroup, induced (restricted) representation
Article copyright: © Copyright 1978 American Mathematical Society