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arXiv · 2207.00802

Subspaces Fixed by a Nilpotent Matrix

Marvin Anas Hahn·Gabriele Nebe·Mima Stanojkovski·Bernd Sturmfels
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Abstract

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.

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Marvin Anas Hahn, Gabriele Nebe, Mima Stanojkovski, Bernd Sturmfels. 2022-07-02. Subspaces Fixed by a Nilpotent Matrix. https://arxiv.org/abs/2207.00802

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