关于 GL(m) 和 GL(m|n) 的舒尔-韦尔对偶性的说明

Pub Date : 2024-09-17 DOI:10.1007/s10468-024-10290-w

František Marko

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引用次数: 0

摘要

我们用统一的基本方法证明了任意特征无限地域上一般线性群和超群的经典、混合、超和混合超舒尔韦耳对偶性的第二部分。这些对偶性分别描述了对称群的群代数和布劳尔壁代数上的张量空间和混合张量空间的内象代数。我们的主要新成果是正特征无限地域上的混合舒尔-韦尔对偶性和混合超舒尔-韦尔对偶性的第二部分。

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A Note on Schur-Weyl Dualities for GL(m) and GL(m|n)

We use a unified elementary approach to prove the second part of classical, mixed, super, and mixed super Schur-Weyl dualities for general linear groups and supergroups over an infinite ground field of arbitrary characteristic. These dualities describe the endomorphism algebras of the tensor space and mixed tensor space, respectively, over the group algebra of the symmetric group and the Brauer wall algebra, respectively. Our main new results are the second part of the mixed Schur-Weyl dualities and mixed super Schur-Weyl dualities over an infinite ground field of positive characteristic.

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