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Quadratic base change for $p$-adic $\mathrm{SL}\left( 2\right) $ as a theta correspondence I: Occurrence

Author(s): David Manderscheid
Journal: Proc. Amer. Math. Soc. 127 (1999), 1281-1288.
MSC (1991): Primary 11F70; Secondary 11F27, 22E50
Posted: January 27, 1999
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Abstract: The local theta correspondence is considered for reductive dual pairs $\left( \mathrm{SL}_{2}\left( F\right) ,\mathrm{O}\left( F\right) \right) $ where $F$ is a $p$-adic field of characteristic zero and $\mathrm{O}$ is the orthogonal group attached to a quaternary quadratic form with coefficients in $F$ and of Witt rank one over $F$. It is shown that certain representations of $\mathrm{SL}_{2}\left( F\right) $ occur in the correspondence.

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Additional Information:

David Manderscheid
Affiliation: Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242
Email: david-manderscheid@uiowa.edu

DOI: 10.1090/S0002-9939-99-04972-2
PII: S 0002-9939(99)04972-2
Received by editor(s): August 13, 1997
Posted: January 27, 1999
Additional Notes: The author's research was supported in part by NSF through grant DMS-9003213 and NSA through grant MDA904-97-1-0046
Communicated by: Dennis A. Hejhal
Copyright of article: Copyright 1999, American Mathematical Society

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