  Let P be a maximal parabolic of a classical group over a field F. Then the
Levi subgroup M is isomorphic to the product of a classical group and a general
linear group, acting on vector spaces X and W, respectively. In this paper we
decompose the unipotent radical N of P under the adjoint action of M, assuming
dim W is less than or equal to dim X and that dim W is even. When F is a local
field, we obtain a Weyl-type integration formula for N.
