  The quantum double Schubert polynomials studied by Kirillov and Maeno, and by
Ciocan-Fontanine and Fulton, are shown to represent Schubert classes in Kim's
presentation of the equivariant quantum cohomology of the flag variety. We
define parabolic analogues of quantum double Schubert polynomials, and show
that they represent Schubert classes in the equivariant quantum cohomology of
partial flag varieties. For complete flags Anderson and Chen have announced a
proof with different methods.
