} \left[  \begin{aligned}   0 \ell - 0 &\longrightarrow \ell \\   0 \ell &\longrightarrow \left\{   \begin{array}{cc}    \ell &\mbox{if $\ell_0$ odd} \\    \ell+0 &\mbox{if $\ell_0$ even}   \end{array}    \right.  \end{aligned}\right.$$ 