  We construct the polynomial induction functor, which is the right adjoint to
the restriction functor from the category of polynomial representations of a
general linear group to the category of representations of its Weyl group. This
construction leads to a representation-theoretic proof of Littlewood's
plethystic formula for the multiplicity of an irreducible representation of the
symmetric group in such a restriction. The unimodality of certain bipartite
partition functions follows.
