Vertex operator algebras and weak Jacobi forms

@article{Krauel2011VertexOA,
  title={Vertex operator algebras and weak Jacobi forms},
  author={Matthew Krauel and G. Mason},
  journal={arXiv: Quantum Algebra},
  year={2011}
}
Let $V$ be a strongly regular vertex operator algebra. For a state $h \in V_1$ satisfying appropriate integrality conditions, we prove that the space spanned by the trace functions Tr$_Mq^{L(0)-c/24}\zeta^{h(0)} ($M$ a $V$-module) is a vector-valued weak Jacobi form of weight 0 and a certain index $ /2$. We discuss refinements and applications of this result when $V$ is holomorphic, in particular we prove that if $g = e^{h(0)}$ is a finite order automorphism then Tr$_V q^{L(0)-c/24}g$ is a… Expand
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