论文标题
对称组的双重性和多键分区代数
Howe duality of the symmetric group and a multiset partition algebra
论文作者
论文摘要
我们介绍多隔板代数，$ {\ rm m \！p} _ {r，k}（x）$，该元素由多键分区索引，其中$ x $是不确定的，$ r $和$ r $和$ k $是非听觉的整数。该代数可以实现为概括分区代数的图表代数。当$ x $的整数更大或等于$ 2r $时，我们表明$ {\ rm m \！ $ 1 \ leq j \ leq k $。我们描述$ {\ rm m \！p} _ {r，k}（x）$，分支规则和其表示形式的限制的表示形式，在$ x $是一个更大或等于$ 2R $的情况下。
We introduce the multiset partition algebra, ${\rm M\!P}_{r,k}(x)$, that has bases elements indexed by multiset partitions, where $x$ is an indeterminate and $r$ and $k$ are non-negative integers. This algebra can be realized as a diagram algebra that generalizes the partition algebra. When $x$ is an integer greater or equal to $2r$, we show that ${\rm M\!P}_{r,k}(x)$ is isomorphic to a centralizer algebra of the symmetric group, $S_n$, acting on the polynomial ring on the variables $x_{ij}$, $1\leq i \leq n$ and $1\leq j\leq k$. We describe the representations of ${\rm M\!P}_{r,k}(x)$, branching rule and restriction of its representations in the case that $x$ is an integer greater or equal to $2r$.
