A Vertex Algebra Commutant for the $βγ$-System and Howe pairs

Details A Vertex Algebra Commutant for the $βγ$-System and Howe pairs A Vertex Algebra Commutant for the $βγ$-System and Howe pairs

2009-09-26

arxiv.org/abs/0909.4835v1

Mathematics

Quantum Algebra

15 pages, No figures. This is our first paper of series on this topic

Scientific paper

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.

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