轱辘单项式的舒尔-韦尔对偶性：通过舒尔代数的方法

Pub Date : 2024-05-23 DOI:10.1007/s00233-024-10434-w

Carlos A. M. André, Inês Legatheaux Martins

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引用次数: 0

摘要

在扩展对称性原理方面，"轱辘单体"（又称对称逆单体）是典型的结构。在本文中，我们在这个单元和经典舒尔代数的扩展之间建立了舒尔-韦尔对偶性，并将其命名为扩展舒尔代数。我们还解释了这与所罗门提出的轱辘单体和一般线性群之间的舒尔-韦尔对偶性之间的关系，并提到了我们的方法的一些优势。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Schur–Weyl dualities for the rook monoid: an approach via Schur algebras

The rook monoid, also known as the symmetric inverse monoid, is the archetypal structure when it comes to extend the principle of symmetry. In this paper, we establish a Schur–Weyl duality between this monoid and an extension of the classical Schur algebra, which we name the extended Schur algebra. We also explain how this relates to Solomon’s Schur–Weyl duality between the rook monoid and the general linear group and mention some advantages of our approach.

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