A Levi subgroup of a parabolic subgroup 
of a reductive
group is a reductive subgroup 
for which the quotient map 
restricts to an isomorphism
on 
. Thus 
, where 
is the unipotent radical. For a block upper triangular
subgroup of 
, the block diagonal matrices form a Levi subgroup.
Different Levi factors of the same parabolic subgroup
are conjugate by its unipotent radical over an algebraically
closed field.
Lie-theoretic assumptions involving every Levi subgroup enter the positive-characteristic geometric Langlands correspondence.
