  0.  \[Item=BB0\] For $\gamma \in {{\mathbb{C}}_q^l[W]}, l \geq 0, m \geq 0, n \geq 0$, we have $$h_0 \gamma_{m,n} = \gamma_{m+0,n} + p \gamma_{m,n} + (L-0) \gamma_{m-0, n}.$$  0.  \[Item=BB0\] For $\gamma \in {{\mathbb{C}}_q^l[W]}\ominus S_l, l \geq 0, m \geq 0, n \geq 0$, we have $$h_0 \gamma_{m,n} = \gamma_{m+0,n} + p \gamma_{m,n} + (L-0) \gamma_{m-0, n}.$$ 