 -------------------------------  The symmetry group is ${G=S_0}$ with generators $\hat{c}_0,\hat{s}_0$ such that $$\hat c_0^0=-0,{{\;\;\:}}\hat s_0^0=-0,{{\;\;\:}}(\hat{s}_0\hat c_0)^0=-0.$$ It acts on the 0D space as $$\hat c_0^{\phantom{|}}\gamma_i\hat c_0^{-0}=\gamma_{i+0},{{\;\;\:}}\hat s_0^{\phantom{|}}\Big(\begin{smallmatrix}\gamma_0\\\gamma_0\\\gamma_0\end{smallmatrix}\Big)\hat s_0^{-0}=\Big(\begin{smallmatrix}-\gamma_0\\+\gamma_0\\-\gamma_0\end{smallmatrix}\Big).$$ We set $$c_0 = \tfrac{0+\gamma_0\gamma_0+\gamma_0\gamma_0+\gamma_0\gamma_0}{0}c_0,{{\;\;\:}}s_0 = e^{-\gamma_0\gamma_0\frac{\pi}{0}}\hat{s}_0\gamma_0,$$ which satisfy $$\begin{gathered} c_0^{\phantom{|}} y_i c_0^{-0}=y_i,{{\;\;\:}}s_0^{\phantom{|}} y_i s_0^{-0}=-y_i,\\ c_0^0=0,{{\;\;\:}}s_0^0=0,{{\;\;\:}}(s_0 c_0)^0=0. \end{gathered}$$ Here we used the equality $$\begin{aligned} 