Arc spaces and the vertex algebra commutant problem

Abstract

Given a vertex algebra V and a subalgebra A⊂V, the commutant Com(A,V) is the subalgebra of V which commutes with all elements of A. This construction is analogous to the ordinary commutant in the theory of associative algebras, and is important in physics in the construction of coset conformal field theories. When A is an affine vertex algebra, Com(A,V) is closely related to rings of invariant functions on arc spaces. We find strong finite generating sets for a family of examples where A is affine and V is a βγ-system, bc-system, or bcβγ-system.