论文标题
分区代数的中心
The Center of the Partition Algebra
论文作者
论文摘要
在本文中，我们表明分区代数$ \ mathcal {a} _ {2k}（δ）$，在半神经案例中，由归一化jucys-murphy元素中的超对称多项式的亚代词给出。对于非偏见的情况，这种子级别显示为中心，尤其是足够大，足以识别$ \ Mathcal {a} _ {2k}（2k}（δ）$的块结构。这允许一个人给出一个替代描述，以便当两个简单的$ \ mathcal {a} _ {2k}（δ）$ - 模块属于同一块时。
In this paper we show that the center of the partition algebra $\mathcal{A}_{2k}(δ)$, in the semisimple case, is given by the subalgebra of supersymmetric polynomials in the normalised Jucys-Murphy elements. For the non-semisimple case, such a subalgebra is shown to be central, and in particular it is large enough to recognise the block structure of $\mathcal{A}_{2k}(δ)$. This allows one to give an alternative description for when two simple $\mathcal{A}_{2k}(δ)$-modules belong to the same block.
