Irreducible Modules over Finite Simple Lie Pseudoalgebras I. Primitive Pseudoalgebras of Type W and S

One of the algebraic structures that has emerged recently in the study of the operator product expansions of chiral fields in conformal field theory is that of a Lie conformal algebra [K]. A Lie pseudoalgebra is a generalization of the notion of a Lie conformal algebra for which C[\partial] is replaced by the universal enveloping algebra H of a finite-dimensional Lie algebra [BDK]. The finite (i.e., finitely generated over H) simple Lie pseudoalgebras were classified in [BDK]. In a series of papers, starting with the present one, we classify all irreducible finite modules over finite simple Lie pseudoalgebras.