A Characterization of Complex Symmetric Weighted Composition Operators on the Fock Space

We characterize all bounded complex symmetric weighted composition operators on the Fock space ${\mathcal{F}}_{\alpha }^2$, without prescribing a conjugation a priori. Our approach uses reproducing kernels and two generating functions. The Taylor coefficients of these functions are eigenvectors of the operator and its adjoint, respectively. The conjugations arising from our construction are anti-linear Gaussian integral operators. Some of them are weighted composition conjugations, whereas others are not.