论文标题
Gelfand- tsetlin-type重量基库，用于所有特殊线性谎言代数表示，与偏斜舒尔函数相对应
Gelfand--Tsetlin-type weight bases for all special linear Lie algebra representations corresponding to skew Schur functions
论文作者
论文摘要
我们概括了$ \ mathfrak {sl}（n，n，\ mathbb {c}）$的有限维度不可约定表示的著名重量基础结构。偏斜舒尔功能。我们的构造使用偏斜形的半圆形tableaux的钻石色的分布晶格，该晶格概括了一些经典的Gelfand--Tsetlin（GT）晶格。我们的构造发生在某些针对半词代数表示POSET模型的程序化研究的背景下，以及由姓名的作者和其他人进行的对称功能。此处概括了该程序方法的一些关键方面。我们的结构的组合和代表性理论应用在这里和其他地方进行。
We generalize the famous weight basis constructions of the finite-dimensional irreducible representations of $\mathfrak{sl}(n,\mathbb{C})$ obtained by Gelfand and Tsetlin in 1950. Using combinatorial methods, we construct one such basis for each finite-dimensional representation of $\mathfrak{sl}(n,\mathbb{C})$ associated to a given skew Schur function. Our constructions use diamond-colored distributive lattices of skew-shaped semistandard tableaux that generalize some classical Gelfand--Tsetlin (GT) lattices. Our constructions take place within the context of a certain programmatic study of poset models for semisimple Lie algebra representations and Weyl group symmetric functions undertaken by the first-named author and others. Some key aspects of the methodology of that program are recapitulated here. Combinatorial and representation-theoretic applications of our constructions are pursued here and elsewhere.
