For the Kashiwara crystal of a highest weight representation of an affine Lie algebra of type A and rank e, with highest weight Λ, there is a labeling by multipartitions and by piecewise-linear paths in the real weight space called Littelmann paths. Both labelings are constructed recursively, but the crystals are isomorphic, so there is a bijection between the labels. We choose a multicharge \((k_{1},\dots ,k_{r})\), with 0 ≤ k₁ ≤ k₂.... ≤ k_r ≤ e − 1. We put k_i in the node at the upper left corner of partition i and let the residues from \(\mathbb {Z}/ e \mathbb {Z}\) increase across rows and decrease down columns. For e = 2, we call a multipartition residue-homogeneous if all nonzero rows end in nodes of the same residue and if partitions with the same corner residue have first rows of the same parity. The multipartition is called strongly residue-homogeneous if each partition ends in a right triangle of whose side has length one less than the first row of the next partition. We give explicit examples, including many of the important case of symmetric groups. We show that such a multipartition corresponds to a Littelmann path which is unidirectional in the sense that the projection of the the main part of the path to the coordinates of the fundamental weights consists of long paths all lying in either the second or fourth quadrant, separated by short paths between fixed integers encoding the number of rows and addable nodes in the multipartition. The path corresponding to a strongly residue-homogeneous multipartition can be constructed non-recursively using only integers describing the multipartition.

对于具有最高权重 Λ的类型A和秩e仿射李代数的最高权重表示的 Kashiwara 晶体，在实权重空间中有一个由多分区和分段线性路径标记的称为 Littelmann 路径。两个标签都是递归构造的，但晶体是同构的，因此标签之间存在双射。我们选择一个多电荷 \((k_{1},\dots ,k_{r})\)，其中 0 ≤ k ₁ ≤ k ₂ .... ≤ k _r ≤ e − 1。我们将k _i放在节点中在分区i 的左上角，让残基从\(\mathbb {Z}/ e \mathbb {Z}\) 跨行增加并向下减少列。对于电子= 2，如果所有非零行都以相同残差的节点结尾，并且如果具有相同角残差的分区具有相同奇偶校验的第一行，我们称多分区残差齐次。如果每个分区都以直角三角形结束，该三角形的边长比下一个分区的第一行小 1，则称多分区为强残差同质的。我们给出了明确的例子，包括许多对称群的重要例子。我们表明，这样的多分区对应于单向的 Littelmann 路径，因为路径的主要部分到基本权重坐标的投影由长路径组成，所有路径都位于第二或第四象限，分开通过固定整数之间的短路径编码多分区中的行数和可添加节点。