On Induced Representations Distinguished by Orthogonal Groups

http://dx.doi.org/10.4153/CMB-2012-008-0
12 pages

  Published:2012-05-17
 

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.