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In J.Bernstein's notes: REPRESENTATION OF P-ADIC GROUPS, he remarked the following result(see P.88): Let $G$ be a reductive group defined over nonarchimedean local field $F$, $P$ parabolic subgroup of $G$ with Levi-decomposition $P=MN$, and $\rho$ be any irreducible smooth representation of $M$. Then $i_{G,M}(\psi \rho)$ is irreducible for generic unramified character $\psi$ of $M$. I want to know the proof, but i haven't found a proof yet. Thanks so much for providing a proof or reference!

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    $\begingroup$ To improve your question, you should recall the notation : $G$ is a $p$-adic reductive group, $M$ a Levi subgroup, and so on ... $\endgroup$ – Paul Broussous Sep 16 '15 at 14:51
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You can find the answer of your question (and any other question of this kind) in the book of Renard "Représentations des groupes réductifs p-adiques" (http://www.math.polytechnique.fr/~renard/Padic.pdf Théorème p.295 of the file).

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  • $\begingroup$ Yes, thanks! p.295 of the file is p.287 of D.Renard's book. $\endgroup$ – chluo Jan 9 '17 at 7:33
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See Theorem 6.6.1 in Casselman's notes titled "Introduction to the theory of admissible representations of $p$-adic groups", available from https://www.math.ubc.ca/~cass/research/pdf/p-adic-book.pdf

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  • $\begingroup$ Thanks! This is the unitary case. J.Bernstein's beautiful argument had implied it. We want to know the general case. $\endgroup$ – chluo Sep 24 '15 at 6:45

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