2-complex symmetric weighted composition operators on Fock space

The aim of the present paper is to completely characterize 2-complex symmetric weighted composition operators $W_{e^{\overline{p}z,az+b}}$ with the conjugations $C$ and $C_{r,s,t}$ defined by $Cf(z)=\overline{f(\overline{z})}$ and $C_{r,s,t}f(z)=t{e}^{sz}\overline{f(\overline{rz+s})}$ on Fock space by building the relations between the parameters $a$, $b$, $p$, $r$, $s$ and $t$. Some examples of such operators are also given.