arXivDaily arXiv每日学术速递 周一至周五更新
arXiv math/0602608math.COmath.GR
收藏

辛格拉斯曼算子的基子集

Base subsets of symplectic Grassmannians

Mark Pankov

备注：
12 pages
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

设$V$和$V'$是域$F$和$F'$上的$2n$维向量空间。还设$Ω: V\times V\to F$和$Ω': V'\times V'\to F'$是非退化辛形式。用$Π$和$Π'$表示相应的$(2n-1)$维射影空间。$Π$和$Π'$的$k$维全迷向子空间的集合分别记为${\mathcal G}_{k}$和${\mathcal G}'_{k}$.相关建筑物的公寓通过所谓的基本子集与${\mathcal G}_{k}$和${\mathcal G}'_{k}$相交。我们表明，每一个映射的${\mathcal G}_{k}$到${\mathcal G}'_{k}$发送基子集的基子集是由一个辛嵌入的$Π$到$Π'$。

英文摘要：

Let $V$ and $V'$ be $2n$-dimensional vector spaces over fields $F$ and $F'$. Let also $Ω: V\times V\to F$ and $Ω': V'\times V'\to F'$ be non-degenerate symplectic forms. Denote by $Π$ and $Π'$ the associated $(2n-1)$-dimensional projective spaces. The sets of $k$-dimensional totally isotropic subspaces of $Π$ and $Π'$ will denoted by ${\mathcal G}_{k}$ and ${\mathcal G}'_{k}$, respectively. Apartments of the associated buildings intersect ${\mathcal G}_{k}$ and ${\mathcal G}'_{k}$ by so-called base subsets. We show that every mapping of ${\mathcal G}_{k}$ to ${\mathcal G}'_{k}$ sending base subsets to base subsets is induced by a symplectic embedding of $Π$ to $Π'$.

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。

↑