Supercuspidal representations and the theta correspondence. II. 𝑆𝐿(2) and the anisotropic 𝑂(3)

Manderscheid, David

doi:10.1090/S0002-9947-1993-1099354-6

Supercuspidal representations and the theta correspondence. II. $\textrm {SL}(2)$ and the anisotropic $\textrm {O}(3)$
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Trans. Amer. Math. Soc. 336 (1993), 805-816 Request permission

Abstract:

A parametrization is given of the local theta correspondence attached to the reductive dual pair $({\text {SL}}_2(F),\;{\text {O}}(F))$ where $F$ is a nonarchimedean local field of odd residual characteristic and ${\text {O}}$ is the orthogonal group of a ternary quadratic form which is anisotropic over $F$. The parametrization is in terms of inducing data. Various lattice models of the oscillator representation are used.

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