# Generic irreducibility of parabolic induction

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!

• To improve your question, you should recall the notation : $G$ is a $p$-adic reductive group, $M$ a Levi subgroup, and so on ... – Paul Broussous Sep 16 '15 at 14:51

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