A Vertex Algebra Commutant for the $\beta\gamma$-System and Howe pairs.

link: http://arxiv.org/abs/0909.4835
Abstract

Analogue to commutants in the theory of associative algebras, one can
construct a new subalgebra of vertex algebra known as a vertex algebra
commutant. In this paper, for the adjoint representation $V$ of Lie algebra
$sl(2,\C)$, we describe a commutant of $\beta\gamma$- System $S(V)$ by giving
its generators, moreover, we get a new Howe pair of vertex algebras.