Irreducible modules over finite simple 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. A Lie pseudoalgebra is a generalization of the notion of a Lie conformal algebra for which C[d] is replaced by the universal enveloping algebra H of a finite-dimensional Lie algebra. The finite (i.e., finitely generated over H) simple Lie pseudoalgebras were classified in our previous work [B.Bakalov, A.D’Andrea, V.G. Kac, Theory of finite pseudoalgebras, Adv. Math. 162 (2001) 1–140]. In a series of papers, starting with the present one, we classify all irreducible finite modules over finite simple Lie pseudoalgebras.