= Crystal tensor-product rule
Write $\varepsilon_i(b)$ and $\varphi_i(b)$ for the numbers of raising and lowering steps of color $i$ available from a vertex of a <crystal basis>. One convention for the <tensor product of crystals> is
$$
\widetilde f_i(a\otimes b)=\begin{cases}\widetilde f_i(a)\otimes b,&\varphi_i(a)>\varepsilon_i(b),\\a\otimes\widetilde f_i(b),&\varphi_i(a)\le\varepsilon_i(b).\end{cases}
$$
The raising operator uses the first factor for $\varphi_i(a)\ge\varepsilon_i(b)$ and the second otherwise. The different strictness makes raising and lowering inverse along every edge. An edge is absent if the chosen <Kashiwara operator> vanishes. Stating the convention is essential when identifying the <highest-weight vectors> as ordered tensor vertices.
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