Arc spaces and the vertex algebra commutant problem

Details Arc spaces and the vertex algebra commutant problem Arc spaces and the vertex algebra commutant problem

2011-12-30

arxiv.org/abs/1201.0161v1

Mathematics

Representation Theory

This paper together with arXiv:1112.6230 corrects and extends the results of arXiv:0807.4764

Scientific paper

Given a vertex algebra V and a subalgebra A of 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 \beta\gamma-system, bc-system, or bc\beta\gamma-system.

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