Arc spaces and the vertex algebra commutant problem

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...

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Bibliographic Details
Published inAdvances in mathematics (New York. 1965) Vol. 277; pp. 338 - 364
Main Authors Linshaw, Andrew R., Schwarz, Gerald W., Song, Bailin
Format Journal Article
LanguageEnglish
Published Elsevier Inc 04.06.2015
Subjects
Arc spaces
Commutant
Coset construction
Differential operators
Howe pair
Invariant theory
Jet schemes
Vertex algebras
Vertex algebras
Differential operators
Commutant
Jet schemes
Invariant theory
Arc spaces
Howe pair
Coset construction
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Summary: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.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2015.03.007