定义仿射划分代数

Pub Date : 2023-02-02 DOI:10.1007/s10468-022-10196-5

Samuel Creedon, Maud De Visscher

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引用次数: 0

摘要

我们通过生成器和关系定义了仿射分治代数，并证明了有关这个新代数的各种基本结果，类似于其他仿射图代数的结果。特别是，我们证明它扩展了对称群与分治代数之间的舒尔-韦尔对偶性。我们还将它与布伦丹（J. Brundan）和巴尔加斯（M. Vargas）最近定义的仿射划分范畴联系起来。此外，我们还证明了这个仿射划分范畴是海森堡范畴的一个完整单模子范畴。

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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Defining an Affine Partition Algebra

We define an affine partition algebra by generators and relations and prove a variety of basic results regarding this new algebra analogous to those of other affine diagram algebras. In particular we show that it extends the Schur-Weyl duality between the symmetric group and the partition algebra. We also relate it to the affine partition category recently defined by J. Brundan and M. Vargas. Moreover, we show that this affine partition category is a full monoidal subcategory of the Heisenberg category.

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