  A class of classical affine W-algebras are shown to be isomorphic as
differential algebras to the coordinate rings of double coset spaces of certain
prounipotent proalgebraic groups. As an application, integrable Hamiltonian
hierarchies associated with them are constructed geometrically, generalizing
the corresponding result of Feigin-Frenkel and Enriquez-Frenkel for the
principal cases.
