For each positive integer n, we introduce a monoidal category \(\mathcal {J}\mathcal {P}(n)\) using a generalization of partition diagrams. When the characteristic of the ground field is either 0 or at least n, we show \(\mathcal {J}\mathcal {P}(n)\) is monoidally equivalent to the full subcategory of Rep(A_n) whose objects are tensor powers of the natural n-dimensional permutation representation of the alternating group A_n.

中文翻译：

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水母分区类别

对于每个正整数n，我们使用分区图的一般化引入一个单面类别\（\ mathcal {J} \ mathcal {P}（n）\）。当地面场的特征为0或至少为n时，我们证明\（\ mathcal {J} \ mathcal {P}（n）\）与对象为的Rep（A _n）的整个子类别单义相等交替群A _n的自然n维排列表示的张量幂。