  Using the skew-symmetry of the differential operators and multiplication
operators in the canonical representations of finite-dimensional classical Lie
algebras, we obtain some noncanonical polynomial representations of the
classical Lie algebras. The representation spaces of all polynomials are
decomposed into irreducible submodules, which are infinite-dimensional. Bases
for the irreducible submodules are constructed. In particular, we obtain some
new infinite-dimensional irreducible modules of symplectic Lie algebras that
are not of highest weight type.
