# Self-dual vertex algebras

Let $(V,Y)$ be a self-dual conformal vertex algebra. For instance, it could be the vertex algebra associated to a positive definite, even, unimodular quadratic form. I look for a formula to compute $$Y(u,z)u^*,$$ where $u\in V$ and $u^*$ is the corresponding element in $V^*$.

• You are unlikely to find an explicit formula that fits the generality of your question. Do you have some generators and their OPEs available? – S. Carnahan Apr 1 '16 at 22:01
• Generators for $V$ ? You can assume that $V$ is lattice algebra – Giulio Apr 2 '16 at 14:37