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

Abstract

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[∂] 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 (Bakalov etal., 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 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.