Let $G$ be a $p$-adic reductive group, and $\pi$ be an irreducible admissible representation of $G$ that is generic, do we know that the contragredient representation of $\pi$ is also generic?

If $G$ is classical group, I know this is true. Thus this question mainly asks exceptional group case.

I think this should be true, but I couldn't find reference for exceptional groups.

Thanks in advance.

  • 2
    $\begingroup$ Sorry to answer my own question, but I think it might be helpful for others. The answer for this questions is yes and the proof is given in the recent preprint of D. Prasad arxiv.org/abs/1705.03262, Lemma 1 section 3. $\endgroup$
    – Q. Zhang
    May 26 '17 at 1:22

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