论文标题
穿孔tableaux：类型$ a_ {n-1} $中的水晶图组合模型
Perforated Tableaux: A Combinatorial Model for Crystal Graphs in Type $A_{n-1}$
论文作者
论文摘要
我们提出了一个称为\ emph {穿孔的tableaux}的组合模型，以研究$ a_ {n-1} $晶体，统一了几个先前研究的组合模型。我们在标准晶体的$ k $ - 折张量产品中识别节点，其中$ k $单词$ [n] = \ {1，\ ldots n \} $。 我们用穿孔的tableaux（ptableaux）对这种晶体进行建模，将此识别均等地识别到biorders，rsk $（p，q）$ tableaux pairs和矩阵型号。在PtableAux设置中，晶体运算符更简单地定义，我们可以在没有计算的情况下视觉识别最高权重。我们将Littlewood-Richardson规则中的张量产品推广到所有$ [n]^{\ otimes k} $中，而不仅仅是不可减至的晶体，它们的阅读单词来自Semistandard Young Tableaux。我们将疏散（Lusztig的相关性）与PtableAux晶体算子的产物联系起来，并找到一种组合算法来计算最高重量ptableaux的换向器。
We present a combinatorial model, called \emph{perforated tableaux}, to study $A_{n-1}$ crystals, unifying several previously studied combinatorial models. We identify nodes in the $k$-fold tensor product of the standard crystal with length $k$ words in $[n]= \{ 1, \ldots n\}$. We model this crystal with perforated tableaux (ptableaux), extending this identification isomorphically to biwords, RSK $(P,Q)$ tableaux pairs, and matrix models. In the ptableaux setting, crystal operators are more simply defined and we can identify highest weights visually without computation. We generalize the tensor products in the Littlewood-Richardson rule to all of $[n]^{\otimes k}$, and not just the irreducible crystals whose reading words come from semistandard Young tableaux. We relate evacuation (Lusztig involution) to products of ptableaux crystal operators, and find a combinatorial algorithm to compute commutators of highest weight ptableaux.
