Commutants of complex symmetric weighted composition operators on Hilbert spaces of analytic functions

We characterize all weighted composition operators v C ψ vCψ that commute with a J μ Jμ -symmetric weighted composition operator u C φ uCφ on the reproducing kernel Hilbert space H γ Hγ of analytic functions on the unit disk D { D} . It turns out these commuting operators v C ψ vCψ are necessarily J μ Jμ -symmetric. Furthermore, we obtain characterization(s) for the commuting operator v C ψ vCψ to be self-adjoint, normal or unitary.