%0 Journal Article
%T A Vertex Algebra Commutant for the $¦Â¦Ã$-System and Howe pairs
%A Yan-Jun Chu
%A Fang Huang
%A Zhu-Jun Zheng
%J Mathematics
%D 2009
%I arXiv
%X Analogue to commutants in the theory of associative algebras, one can construct a new subalgebra of vertex algebra known as a vertex algebra commutant. In this paper, for the adjoint representation $V$ of Lie algebra $sl(2,\C)$, we describe a commutant of $\beta\gamma$- System $S(V)$ by giving its generators, moreover, we get a new Howe pair of vertex algebras.
%U http://arxiv.org/abs/0909.4835v1