论文标题
由nilpotent矩阵固定的子空间
Subspaces Fixed by a Nilpotent Matrix
论文作者
论文摘要
由给定的nilpotent $ n \ times n $矩阵固定的线性空间形成了格拉斯曼尼亚的子不同。我们将这些品种分类为小$ n $。 Mutiah，Weekes和Yacobi猜想它们的自由基理想是由某些线性形式称为洗牌方程产生的。我们证明了$ n \ leq 7 $的猜想，并以$ n = 8 $反驳了它。源自杂草植物的nilpotent矩阵，这个问题仍然是开放的。
The linear spaces that are fixed by a given nilpotent $n \times n$ matrix form a subvariety of the Grassmannian. We classify these varieties for small $n$. Mutiah, Weekes and Yacobi conjectured that their radical ideals are generated by certain linear forms known as shuffle equations. We prove this conjecture for $n \leq 7$, and we disprove it for $n=8$. The question remains open for nilpotent matrices arising from the affine Grassmannian.
