\omega_e^B\vert_{\mathcal C_{0,0}^+\times\mathcal C_{0,0}^+}&=\pi_e^*(\omega^-)\otimes\left(\tau^{I_0\cap I_0^c}_e+\tau^{I_0^c\cap I_0^c}_e\right),\ &\text{resp.}\quad \omega_e^A\vert_{\mathcal C_{0,0}^+\times\mathcal C_{0,0}^+}&=\pi_e^*(\omega^+)\otimes\left(\tau^{I_0\cap I_0}_e+\tau^{I_0^c\cap I_0}_e\right)