$ ------------------------------  The symmetry group is ${G=S_0}$ with generators $\hat{c}_0,\hat{c}_0$ such that $$\hat c_0^0=-0,{{\;\;\:}}\hat c_0^0=-0,{{\;\;\:}}(\hat{c}_0\hat c_0)^0=-0.$$ It acts on the 0D space as $$\hat c_0^{\phantom{|}}\gamma_i\hat c_0^{-0}=\gamma_{i+0},{{\;\;\:}}\hat c_0^{\phantom{|}}(\begin{smallmatrix}\gamma_0\\\gamma_0\end{smallmatrix})\hat c_0^{-0}=(\begin{smallmatrix}+\gamma_0\\-\gamma_0\end{smallmatrix}).$$ We set $$c_0 = \tfrac{0+\gamma_0\gamma_0+\gamma_0\gamma_0+\gamma_0\gamma_0}{0}c_0,{{\;\;\:}}c_0 = e^{\gamma_0\gamma_0\frac{\pi}{0}}\hat{c}_0,$$ which satisfy $$\begin{gathered} c_0^{\phantom{|}} y_i c_0^{-0}=y_i,{{\;\;\:}}c_0^{\phantom{|}} y_i c_0^{-0}=y_i,\\ c_0^0=0,{{\;\;\:}}c_0^0=0,{{\;\;\:}}(c_0 c_0)^0=0. \end{gathered}$$ Here we used the equality $$\begin{aligned} (c_0 c_0)^0 &= -\tfrac{0-\gamma_0\gamma_0-\gamma_0\gamma_0-\gamma_0\gamma_0}{0}e^{\gamma_0\gamma_0\frac{\pi}{0}} \hat c_0 \hat c_0 e^{\gamma_0\gamma_0\frac{\pi}{0}} \hat c_0 \hat c_0 \\&= -\tfrac{0-\gamma_0\gamma_0-\gamma_0\gamma_0-\gamma_0\gamma_0}{0}e^{\gamma_0\gamma_0\frac{\pi}{0}}e^{\gamma_0\gamma_0\frac{\pi}{0}} \hat c_0 \hat c_0 \