A Hilbert theorem for vertex algebras

Andrew R. Linshaw
Arxiv ID: 0903.3814Last updated: 8/10/2020
Given a simple vertex algebra A and a reductive group G of automorphisms of 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 W_{1+\infty} 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.

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