Howe Pairs in the Theory of Vertex Algebras

Bong H. Lian Brandeis University Andrew R. Linshaw University of California, San Diego

Representation Theory mathscidoc:1608.30001

Journal of Algebra, 317, 111-152 , 2007
For any vertex algebra V and any subalgebra A of V, there is a new subalgebra of V known as the commutant of A in V. This construction was introduced by Frenkel-Zhu, and is a generalization of an earlier construction due to Kac-Peterson and Goddard-Kent-Olive known as the coset construction. In this paper, we interpret the commutant as a vertex algebra notion of invariant theory. We present an approach to describing commutant algebras in an appropriate category of vertex algebras by reducing the problem to a question in commutative algebra. We give an interesting example of a Howe pair (ie, a pair of mutual commutants) in the vertex algebra setting.
Howe Pairs, Vertex Algebras
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  title={Howe Pairs in the Theory of Vertex Algebras},
  author={Bong H. Lian, and Andrew R. Linshaw},
  booktitle={Journal of Algebra},
  pages={111-152 },
Bong H. Lian, and Andrew R. Linshaw. Howe Pairs in the Theory of Vertex Algebras. 2007. Vol. 317. In Journal of Algebra. pp.111-152 .
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