论文标题
$ sp（n）$ - grassmannians of Complex的轨道和Hermitian Quaternionic矢量空间的$σ$ -COMPERX子空间
$Sp(n)$-orbits in the Grassmannians of complex and $Σ$-complex subspaces of an Hermitian quaternionic vector space
论文作者
论文摘要
我们确定了$ sp（n）$ - 轨道的不变性，其中$ 2K $ dimensional Complex和$σ$ complex子空间的真正Grassmannian $ gr^\ r（2k，4n）$的$ 4N $ -Dimensional-Dipensional hermitian hermitian Quaternic Quaternionic Quaternicic vector vector Space。 $σ$ - 复合子空间是复杂子空间的正交总和，而不是符号，兼容的复杂结构。结果是通过考虑此类子空间的两个主要特征来获得的。首先是，任何此类子空间都承认4维复合物加成的Hermitian正交总和，如果$ k $奇怪，则承认了4维复合物加上加和2维完全复杂的子空间的分解，这意味着加音的Quatternionsivals成对是正交的。第二个是任何4维复合物加成$ u $都是同类子空间，即对任何兼容的复杂结构$ a $ $ a $的$（u，au）$的主要角度都相同。使用这些属性，我们确定了$ gr^\ r（2k，4n）$的此类子空间的$ sp（n）$轨道的完整集合。
We determine the invariants characterizing the $Sp(n)$-orbits in the real Grassmannian $Gr^\R(2k,4n)$ of the $2k$-dimensional complex and $Σ$-complex subspaces of a $4n$-dimensional Hermitian quaternionic vector space. A $Σ$-complex subspace is the orthogonal sum of complex subspaces by different, up to sign, compatible complex structure. The result is obtained by considering two main features of such subspaces. The first is that any such subspace admits a decomposition into an Hermitian orthogonal sum of 4-dimensional complex addends plus a 2-dimensional totally complex subspace if $k$ is odd, meaning that the quaternionification of the addends are orthogonal in pairs. The second is that any 4-dimensional complex addend $U$ is an isoclinic subspace i.e. the principal angles of the pair $(U,AU)$ are all the same for any compatible complex structure $A$. Using these properties we determine the full set of the invariants characterizing the $Sp(n)$-orbit of such subspaces in $Gr^\R(2k,4n)$.
