论文标题
矩阵和分区的多项式不变，Brauer代数
Polynomial invariants on matrices and partition, Brauer algebra
论文作者
论文摘要
我们确定对称组$ \ mathfrak {s} _d $的中心设备的尺寸$ D $箭头。 Using Schur-Weyl duality as a fundamental theory, we conclude that each centralizer is related with the $G$-invariant space $P^d(M_n(\mathbf{k}))^G$ of degree $d$ homogeneous polynomials on $n \times n$ matrices, where $G$ is the orthogonal group and the group of permutation matrices, respectively.我们的方法提供了一种统一的方式来表明$ p^d的尺寸（m_n（\ mathbf {k}））^g $对于足够大的$ n $而言是稳定的。
We identify the dimension of the centralizer of the symmetric group $\mathfrak{S}_d$ in the partition algebra $\mathcal{A}_d(δ)$ and in the Brauer algebra $\mathcal{B}_d(δ)$ with the number of multidigraphs with $d$ arrows and the number of disjoint union of directed cycles with $d$ arrows, respectively. Using Schur-Weyl duality as a fundamental theory, we conclude that each centralizer is related with the $G$-invariant space $P^d(M_n(\mathbf{k}))^G$ of degree $d$ homogeneous polynomials on $n \times n$ matrices, where $G$ is the orthogonal group and the group of permutation matrices, respectively. Our approach gives a uniform way to show that the dimensions of $P^d(M_n(\mathbf{k}))^G$ are stable for sufficiently large $n$.
