A Hilbert theorem for vertex algebras

Given a simple vertex algebra A, the invariant subalgebra A(G) is strongly finitely generated in most examples where its structure is known. This phenomenon is subtle, and is generally not true of the classical limit of A(G), which often requires infinitely many generators and infinitely many relations to describe. Using tools from classical invariant theory, together with recent results on the structure of the W1+infinity algebra, we establish the strong finite generation of a large family of invariant subalgebras of beta gamma-systems, bc-systems, and bc beta gamma-systems.