关于平稳实矩阵施布特簇的研究
On stationary real matrix Schubert varieties
AI总结：
本文研究了实矩阵施布特簇的平稳性，证明了特定条件下其极小性，并揭示了相关簇的结构特性。
摘要：
在本文中，我们研究了实矩阵施布特簇在第一变分下的平稳性条件。我们首先证明，其开稠密正则部分成为极小子流形的必要条件是相应的部分排列是 vexillary 的。在 vexillary 的部分排列中，我们通过几何论证证明，当罗特图是格拉斯曼型且至多有两个连通分量时，其极小性成立。我们进一步得出结论，那些分解为这种类型乘积的簇也是极小的。这些簇包括所有行列式簇以及一些新的极小锥。
英文摘要：
In this paper, we study when a real matrix Schubert variety is stationary with respect to the first variation. We first show that a necessary condition for its open dense regular part to be a minimal submanifold is that the corresponding partial permutation is vexillary. Among vexillary partial permutations, we establish minimality by a geometric argument when the Rothe diagram is of Grassmannian type and has at most two connected components. We further obtain, as a corollary, the minimality of those varieties that decompose as products of this type. These varieties include all determinantal varieties as well as some new minimal cones.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
