Abstract:We prove that the kernel of the action of the group algebra of the Weyl group acting on tensor space (via restriction of the action from the general linear group) is a cell ideal with respect to the alternating Murphy basis. This provides an analogue of the second fundamental theory of invariant theory for the partition algebra over an arbitrary commutative ring and proves that the centraliser algebras of the partition algebra are cellular. We also prove similar results for the half partition algebras.

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中文翻译：

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分区代数不变论的一个积分第二基本定理

摘要：我们证明了外尔群的群代数作用于张量空间的核（通过对一般线性群的作用的限制）是关于交替墨菲基的细胞理想。这为任意交换环上的划分代数提供了不变量理论的第二基本理论的类似物，并证明了划分代数的中心化代数是细胞的。我们还证明了半分区代数的类似结果。

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