双拉格朗日格拉斯曼流形的几何
Geometry of bi-Lagrangian Grassmannian
AI总结：
本文研究实复向量空间上2-形式束的双拉格朗日格拉斯曼流形结构，将其简化为同特征值若尔当块的束分析，等价于幂零自伴算子不变拉格朗日子空间研究，计算了维数并刻画了三类情形的自同构轨道。
摘要：
本文探究实或复向量空间上2-形式束的bi-Lagrangian Grassmannian（双拉格朗日格拉斯曼流形）的结构。我们将分析简化为若尔当-克罗内克典范形由具有相同特征值的若尔当块构成的束。我们证明这等价于研究在幂零自伴算子下不变的拉格朗日子空间。我们计算了bi-Lagrangian Grassmannian的维数，并描述了其在自同构群下的开轨道。我们完全描述了以下三种情形的自同构轨道：单个若尔当块、相等若尔当块的和以及两个不同若尔当块的和。
英文摘要：
This paper explores the structure of bi-Lagrangian Grassmanians for pencils of $2$-forms on real or complex vector spaces. We reduce the analysis to the pencils whose Jordan-Kronecker Canonical Form consists of Jordan blocks with the same eigenvalue. We demonstrate that this is equivalent to studying Lagrangian subspaces invariant under a nilpotent self-adjoint operator. We calculate the dimension of bi-Lagrangian Grassmanians and describe their open orbit under the automorphism group. We completely describe the automorphism orbits in the following three cases: for one Jordan block, for sums of equal Jordan blocks and for a sum of two distinct Jordan blocks.
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。
