A parabolic subgroup of a connected reductive group over an algebraically closed field
is a closed subgroup containing a Borel
subgroup. Equivalently, the quotient by that subgroup is a projective algebraic
variety. For 
,
a parabolic subgroup is the stabilizer of a flag of vector subspaces. The Borel
subgroup of upper triangular matrices stabilizes a complete flag.
A parabolic subgroup 
has a unipotent radical 
and a Levi subgroup 
with 
. Vanishing of constant terms along every proper parabolic
subgroup defines cuspidal automorphic
representations.
