论文标题
Cohen-Macaulay Specht理想的规律性
Regularity of Cohen-Macaulay Specht ideals
论文作者
论文摘要
对于{\ mathbb n} $中的分区$λ$，让$ i^{\ rm sp}_λ$是$ r = k [x_1，\ ldots，x_n] $的理想的理想。在上一篇论文中，第二作者表明，如果$ r/i^{\ rm sp}_λ$是cohen-macaulay，那么$λ$是$（n-d，1，\ ldots，1），（n-d，d）$或$（n-d）$或$（d，d，d，d，d，d，1）$，并且如果$ car car car car car）= 0 $ car）= 0 $。在本文中，我们计算了$ r/i^{\ rm sp}_λ$的希尔伯特系列$λ=（n-d，d）$或$（d，d，d，d，1）$。因此，当它是Cohen-Macaulay时，我们获得了$ r/i^{\ rm sp}_λ$的Castelnuovo-Mumford的规律性。特别是，$ i^{\ rm sp} _ {（d，d，d，1）} $在Cohen-Macaulay案例中具有$（d+2）$ - 线性分辨率。
For a partition $λ$ of $n \in {\mathbb N}$, let $I^{\rm Sp}_λ$ be the ideal of $R=K[x_1,\ldots,x_n]$ generated by all Specht polynomials of shape $λ$. In the previous paper, the second author showed that if $R/I^{\rm Sp}_λ$ is Cohen-Macaulay, then $λ$ is either $(n-d,1,\ldots,1),(n-d,d)$, or $(d,d,1)$, and the converse is true if ${\rm char}(K)=0$. In this paper, we compute the Hilbert series of $R/I^{\rm Sp}_λ$ for $λ=(n-d,d)$ or $(d,d,1)$. Hence, we get the Castelnuovo-Mumford regularity of $R/I^{\rm Sp}_λ$, when it is Cohen-Macaulay. In particular, $I^{\rm Sp}_{(d,d,1)}$ has a $(d+2)$-linear resolution in the Cohen-Macaulay case.
