论文标题
关于最大未成年人和亚最大PFAFFIAN的广义多重性
On the generalized multiplicities of maximal minors and sub-maximal pfaffians
论文作者
论文摘要
令$ s = \ mathbb {c} [x_ {ij}] $为$ m \ times n $ no $通用变量的多项式环（分别$（2n+1）\ times（2n+1）\ skew-Ammetric variables的多项式环比$ \ mathbb c} $（c} $（c c} $）$（$ skew-Metsirric viaiables）。 $ s $的未成年人（分别是最大PFAFFIANS）。利用Raicu等人的工作中引入的表示理论技术，我们研究了确定性和PFAFFIAN增厚的局部共同体学模块长度的渐近行为，以选择合适的共同体学度。这种渐近行为也被定义为乘以众所周知的概念。我们表明，环境中的多重性与司法和正交的格拉斯曼尼亚人的程度相吻合。
Let $S=\mathbb{C}[x_{ij}]$ be a polynomial ring of $m\times n$ generic variables (resp. a polynomial ring of $(2n+1) \times (2n+1)$ skew-symmetric variables) over $\mathbb{C}$ and let $I$ (resp. Pf) be the determinantal ideal of maximal minors (resp. sub-maximal pfaffians) of $S$. Using the representation theoretic techniques introduced in the work of Raicu et al, we study the asymptotic behavior of the length of the local cohomology module of determinantal and pfaffian thickenings for suitable choices of cohomological degrees. This asymptotic behavior is also defined as a notion of multiplicty. We show that the multiplicity in our setting coincides with the degrees of Grassmannian and Orthogonal Grassmannian.
