 Crystal tensor-product rule

Write ${\epsilon }_i(b)$ and ${\phi }_i(b)$ 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 isThe raising operator uses the first factor for ${\phi }_i(a)\ge {\epsilon }_i(b)$ 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.