  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[\partial] 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. 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 W or S 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 K, 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.
