Cuspidal representation of a finite reductive group
= Cuspidal representation of a finite reductive group
An irreducible complex $G^F$-module is cuspidal if its <Harish-Chandra restriction> is zero for every proper rational <parabolic subgroup>. By adjunction, it occurs in no <Harish-Chandra induction> from a proper rational <Levi subgroup>. This is a finite-group notion, distinct from a cuspidal automorphic representation.