Let $G$ be a reductive p-adic group, $\pi$ a complex smooth representation of $G$. Then it is known that if $\pi$ is irreducible, then it is admissible.


I need help to find a reference for this fact, and want to know if it is true for real reductive group. Thanks a lot.



reference help: irreducible implies admissible
1) In these lecture notes:


<http://www.math.tau.ac.il/~bernstei/Unpublished_texts/unpublished_texts/Bernstein93new-harv.lect.from-chic.pdf>


you have theorem 12, on page 37. He does it for GL\_n I think, but it should be similar for other groups...


2) For a real group, I think you should be more specific. There is Soergel's counter-example in the paper "An Irreducible not Admissible Banach Representation of $SL(2, \mathbb{R})$".


