For split groups over a $p$-adic field, every irreducible smooth (complex) representation is either infinite-dimensional or one-dimensional. Is it true for quasisplit groups that split over an unramified extension, or quasisplit groups in general? Unfortunately I don't have a good feel for examples, since the books I consult for learning the representation theory of $p$-adic groups usually stick to groups like $GL\_n$.



Finite dimensional irreducible representations of quasisplit p-adic groups
See Prop. 3.9 of <http://math.stanford.edu/~conrad/JLseminar/Notes/L2.pdf> for an optimal affirmative answer (no quasi-split condition needed: any connected reductive group over any non-archimedean local field, with the minimal necessary isotropicity hypotheses).


