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On Induced Representations Distinguished by Orthogonal Groups

Published online by Cambridge University Press:  20 November 2018

Cesar Valverde
Cesar Valverde*
Affiliation:
Department of Mathematics and Computer Science, Rutgers University, Newark, NJ 07102-1811 e-mail: [email protected]
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Abstract.

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Let $F$ be a local non-archimedean field of characteristic zero. We prove that a representation of $GL\left( n,\,F \right)$ obtained from irreducible parabolic induction of supercuspidal representations is distinguished by an orthogonal group only if the inducing data is distinguished by appropriate orthogonal groups. As a corollary, we get that an irreducible representation induced from supercuspidals that is distinguished by an orthogonal group is metic.

Keywords

22E50distinguished representationparabolic induction
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 3 , 01 September 2013 , pp. 647 - 658
Copyright
Copyright © Canadian Mathematical Society 2013

References

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