In mathematics, a mirabolic subgroup of the general linear group GLn(k) is a subgroup consisting of automorphisms fixing a given non-zero vector in kn.
Mirabolic subgroups were introduced by (Gelfand & Kajdan 1975).
The image of a mirabolic subgroup in the projective general linear group is a parabolic subgroup consisting of all elements fixing a given point of projective space.
The word "mirabolic" is a portmanteau of "miraculous parabolic".
The mirabolic subgroup is used to define the Kirillov model of a representation of the general linear group.