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# On Induced Representations Distinguished by Orthogonal Groups

Published:2012-05-17
Printed: Sep 2013
• Cesar Valverde,
Department of Mathematics and Computer Science, Rutgers University, Newark, NJ 07102-1811
 Format: LaTeX MathJax PDF

## Abstract

Let $F$ be a local non-archimedean field of characteristic zero. We prove that a representation of $GL(n,F)$ 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: distinguished representation, parabolic induction
 MSC Classifications: 22E50 - Representations of Lie and linear algebraic groups over local fields [See also 20G05]

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