论文标题
订购的设定分区，Garsia-Procesi模块和等级品种
Ordered set partitions, Garsia-Procesi modules, and rank varieties
论文作者
论文摘要
我们介绍了一个理想的家族$ i_ {n，λ，s} $ in $ \ mathbb {q} [x_1，\ dots，x_n] $ for $λ$ a $ k \ leq n $和integer $ s \ s \ geq \ geq \ ell（λ）$的分区。这个家庭既包含Tanisaki Ideals $i_λ$又包含Haglund-Rhoades-Shimozono的理想$ i_ {n，k} $作为特殊情况。我们将相应的商戒指$ r_ {n，λ，s} $作为对称组模块。当$ n = k $和$ s $是任意的时，我们恢复了garsia-procesi模块，当$λ=（1^k）$和$ s = k $时，我们恢复了haglund-rhoades-rhoades-rhoades-rhoades-rhoades-rhoades-shimozono的广义共同代数。我们给出了$ r_ {n，λ，s} $的单一基础，统一了Garsia-procesi和Haglund-rhoades-shimozono研究的单一基础，并在$ r_ {n，λ，s} $的$（n，s）$（n，n，s）$（n，s）$（n，s）上的$ r_ {n，λ，s} $的$ s_n $ module结构实现。我们还证明了希尔伯特系列的公式，并将$ r_ {n，λ，s} $的Frobenius特征分级。然后，我们使用Weyman的结果将工作与Eisenbud-Saltman等级品种联系起来。作为我们工作的应用，我们给出了单一基础，希尔伯特系列公式，并为方案理论相交的坐标环与对角线矩阵的坐标环分级。
We introduce a family of ideals $I_{n,λ,s}$ in $\mathbb{Q}[x_1,\dots,x_n]$ for $λ$ a partition of $k\leq n$ and an integer $s \geq \ell(λ)$. This family contains both the Tanisaki ideals $I_λ$ and the ideals $I_{n,k}$ of Haglund-Rhoades-Shimozono as special cases. We study the corresponding quotient rings $R_{n,λ,s}$ as symmetric group modules. When $n=k$ and $s$ is arbitrary, we recover the Garsia-Procesi modules, and when $λ=(1^k)$ and $s=k$, we recover the generalized coinvariant algebras of Haglund-Rhoades-Shimozono. We give a monomial basis for $R_{n,λ,s}$, unifying the monomial bases studied by Garsia-Procesi and Haglund-Rhoades-Shimozono, and realize the $S_n$-module structure of $R_{n,λ,s}$ in terms of an action on $(n,λ,s)$-ordered set partitions. We also prove formulas for the Hilbert series and graded Frobenius characteristic of $R_{n,λ,s}$. We then connect our work with Eisenbud-Saltman rank varieties using results of Weyman. As an application of our work, we give a monomial basis, Hilbert series formula, and graded Frobenius characteristic formula for the coordinate ring of the scheme-theoretic intersection of a rank variety with diagonal matrices.
