I am wondering why the first well known example of non-tempered irreducible admissible representation of $p$-adic group $U(n)$ should be $U(3)$. Because, Gelbart and Rogawski suggested the non-tempered representation of $U(3)$ using the theta lift.


I know all irreducible representation of $U(1)$ should be tempered because $U(1)$ is compact. But why isn't there known example for the non-tempered representation of $U(2)$? I think it should be there.



Is there a non-tempered representation of U(2)?
The admissible representations of U(2) over a p-adic field are fairly straightforward since they essentially come from those of SL(2) or a the norm one elements of the quaternions. 


Let me add (two days later) that the point is not that the representation of U(3) that arises from the theta-lift is non-tempered but rather that is non-tempered AND the way it arises from a theta-lift. This allows you to construct CAP representations of U(3) globally. 


