Tensor products for 𝑆𝐿(2,𝑘)

Martin, Robert P.

doi:10.1090/S0002-9947-1978-0487045-3

Tensor products for $\textrm {SL}(2, k)$
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by Robert P. Martin PDF

Trans. Amer. Math. Soc. 239 (1978), 197-211 Request permission

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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