Smooth representation of a locally profinite group
= Smooth representation of a locally profinite group
= Smooth representation
{synonym}
A complex <group representation> $\pi:G\to\operatorname{GL}(V)$ is smooth when every vector is fixed by some <compact-open subgroup>. Equivalently each vector's stabilizer is open. Smoothness is local constancy of orbit maps with the vector space regarded discretely, not ordinary continuity into a finite-dimensional complex topology.