  Let G be a Coxeter group of type A_n, B_n, D_n or I_2(N), or a complex
reflection group of type G(de,e,n). Let V be its standard representation and
let k be an integer greater than 2. Then G acts on S(V)^{\otimes k}. We show
that the algebra of invariants (S(V)^{\otimes k})^G is a free (S(V)^G)^{\otimes
k}-module of rank |G|^{k-1}, and that S(V)^{\otimes k} is not a free
(S(V)^{\otimes k})^G-module.
