@article{Lian2006HowePI,
title={Howe pairs in the theory of vertex algebras},
author={B. Lian and A. Linshaw},
journal={Journal of Algebra},
year={2006},
volume={317},
pages={111-152}
}

Abstract For any vertex algebra V and any subalgebra A ⊂ 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… Expand