Transactions of the American Mathematical Society

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



Supercuspidal representations and the theta correspondence. II. $ {\rm SL}(2)$ and the anisotropic $ {\rm O}(3)$

Author: David Manderscheid
Journal: Trans. Amer. Math. Soc. 336 (1993), 805-816
MSC: Primary 22E50; Secondary 11F70
MathSciNet review: 1099354
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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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Article copyright: © Copyright 1993 American Mathematical Society