Classification of p-adic representations

Question

I am studying this paper https://arxiv.org/pdf/1412.0737.pdf . The classification in theorems 1-3 is extremely elegant, but from what I understand it is implied from this paper specifically for mod $p$ representations where $p$ equals the characteristic of the field over which the group is defined. Doesn't the same classification hold for complex representations? And/or representations over other characteristics $l$? If yes, do you have any good references for that?

Answer 1

Update: I could be mistaken, but it seems that the answer above is not correct. This classification for complex representation apparently is called Bernstein-Zelevinsky classification, it was established in their important 70s-80s papers, and it holds only for $GL_n$. For other classical groups, for complex representations, I think that there are even counterexamples. For mod $l$ representations I am not sure what holds, as the Vigneras paper is in French and I am not convenient with them.

I am posting this so that other people are not confused by this thread, but I hope that someone more knowledgeable (i.e. practically anybody) will clarify the situation more.