Irreducible modules over finite simple Lie pseudoalgebras II. Primitive pseudoalgebras of type KK

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[∂]C[∂] is replaced by the universal enveloping algebra HH of a finite-dimensional Lie algebra. The finite (i.e., finitely generated over HH) simple Lie pseudoalgebras were classified in our previous work (Bakalov et al., 2001) [2]. The present paper is the second in our series on representation theory of simple Lie pseudoalgebras. In the first paper we showed that any finite irreducible module over a simple Lie pseudoalgebra of type WW or SS is either an irreducible tensor module or the kernel of the differential in a member of the pseudo de Rham complex. In the present paper we establish a similar result for Lie pseudoalgebras of type KK, with the pseudo de Rham complex replaced by a certain reduction called the contact pseudo de Rham complex. This reduction in the context of contact geometry was discovered by Rumin.