In this paper, we investigate Hermitian weighted composition operators on the Hardy space \({H}^{2}({{\mathbb D}^{2}})\) over the bidisk \({{\mathbb D}^{2}}\) . Concretely, we characterize Hermitian weighted composition operators Cψ,φ on \({H}^{2}({{\mathbb D}^{2}})\) into two classes. To our surprise, we find that φ1 and φ2 are depending only on one variable in each class, where φ = (φ1, φ2). Moreover, spectra and spectral decompositions of Hermitian weighted composition operators are described. In addition, semigroups of weighted composition operators over the bidisk are studied. Our results extend those of Cowen and Ko [Trans. Amer. Math. Soc., 362, 5771–5801 (2010)].
