Plasmon-induced transparency (PIT) is a class of electromagnetically induced transparency phenomena that enhances the interaction between light and matter, thereby improving the performance of nano-optical devices. However, conventional PITs usually rely on near-field coupling between bright and dark modes. In order to break through the limitation of this mechanism, this study proposes a dual-polarized graphene hypersurface structure, which consists of four groups of symmetric L-shaped graphene surrounding cross-shaped hollow graphene, forming a triple PIT through the synergistic effect between two single PITs. The accuracy of the results is verified by simulating the transmission spectra by Finite-difference time-domain(FDTD), which is highly similar to the coupled-mode theory(CMT) results. It is found that the structure exhibits a group refractive index of up to 500 as a slow-light device with excellent slow-light modulation through modulation of Fermi energy levels and carrier mobility. As a polarization device, the structure has dual polarization properties, producing a triple PIT window at the incidence of both x and y polarized light. In particular, the resonant frequency f₆ is not affected by the direction of polarization of the incident light. This good stability and immunity to interference in different polarized light is particularly important for the design of polarization devices. Meanwhile, we adjusted the length parameter of graphene L₂ and found that the resonance frequency f₆ remained highly stable, showing a better tolerance to structural changes. Therefore, in this study, a multifunctional integrated device with slow light modulation and polarization selection in one device is designed to provide new theoretical guidance and research direction for synergistic effect based on polarization insensitivity.