On the SL(2) period integral

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Let E/F be a quadratic extension of number fields. For a cuspidal representation $π$ of SL(2,A_E), we study the non-vanishing of the period integral on SL(2,F)\SL(2,A_F). We characterise the non-vanishing of the period integral of $π$ in terms of $π$ being generic with respect to characters of E\A_E which are trivial on A_F. We show that the period integral in general is not a product of local invariant functionals, and find a necessary and sufficient condition when it is. We exhibit cuspidal representations of SL(2,A_E) whose period integral vanishes identically while each local constituent admits an SL(2)-invariant linear functional. Finally, we construct an automorphic representation $π$ on SL(2,A_E) which is abstractly SL(2,A_F) distinguished but none of the elements in the global L-packet determined by $π$ is distinguished by SL(2,A_F).

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Number Theory, Representation Theory, 11F70; 22E55

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http://salesiana.dossiersoluciones.com/handle/123456789/100976

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0412213
 http://arxiv.org/abs/math/0412213

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arXiv