Quadratic base change for <IMG ALIGN=MIDDLE HEIGHT=32 WIDTH=50> as a theta correspondence I: Occurrence期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Quadratic base change for as a theta correspondence I: Occurrence

Authors:	David Manderscheid

Institution:	Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242

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 is a -adic field of characteristic zero and $\mathrm{O}$ is the orthogonal group attached to a quaternary quadratic form with coefficients in and of Witt rank one over . It is shown that certain representations of $\mathrm{SL}_{2}\left( F\right)$ occur in the correspondence.

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