Irreducible representations of simple Lie algebras by differential operators

We describe a systematic method to construct arbitrary highest-weight modules, including arbitrary finite-dimensional representations, for any finite dimensional simple Lie algebra g. The Lie algebra generators are represented as first order differential operators in $\frac{1}{2}$ (dim g - rank g) variables. All rising generators e are universal in the sense that they do not depend on representation, the weights enter (in a very simple way) only in the expressions for the lowering operators f. We present explicit formulas of this kind for the simple root generators of all classical Lie algebras.