Abstract

We define a graded graph, called the Schur–Weyl graph, which arises naturally when one considers simultaneously the RSK algorithm and the classical duality between representations of the symmetric and general linear groups. As one of the first applications of this graph, we give a new proof of the completeness of the list of discrete indecomposable characters of the infinite symmetric group.

中文翻译：

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Schur-Weyl 图和 Thoma 定理

摘要

我们定义了一个分级图，称为 Schur-Weyl 图，当人们同时考虑 RSK 算法以及对称和一般线性群的表示之间的经典对偶性时，它自然会出现。作为该图的第一个应用之一，我们给出了无限对称群的离散不可分解特征列表的完整性的新证明。