Let $(V,Y)$ be a selfdual 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 $V^*$.

$\begingroup$ You are unlikely to find an explicit formula that fits the generality of your question. Do you have some generators and their OPEs available? $\endgroup$ – S. Carnahan♦ Apr 1 '16 at 22:01

$\begingroup$ Generators for $V$ ? You can assume that $V$ is lattice algebra $\endgroup$ – Giulio Apr 2 '16 at 14:37