论文标题
与有限级自行接合运算符的共轭类别相关的广义格拉曼图
Generalized Grassmann graphs associated to conjugacy classes of finite-rank self-adjoint operators
论文作者
论文摘要
如果有限等级$ m $的两个不同的预测是相邻的，如果它们的差异是第二等级的运营商，或者等效地，其图像的交集为$（M-1）$ - 尺寸。我们将这种邻接关系扩展到有限级自动接合操作员的其他结合类别，从而导致Grassmann图的自然概括。令$ {\ Mathcal C} $是由有限级自行接合运算符组成的，其特征性的尺寸大于$ 1 $。假设来自$ {\ Mathcal C} $的运营商至少具有三个特征值，我们证明，相应的广义Grassmann图的每一个自动形态都是由单一或反独立的操作员引起的自动形态的组成，并且是从同一尺寸的eigensions置换中获得的。 $ {\ Mathcal C} $的运营商只有两个特征值的情况被古典的Chow定理所涵盖，该定理说，没有保留正交性的半线性自动形态引起的图形自动形态。
Two distinct projections of finite rank $m$ are adjacent if their difference is an operator of rank two or, equivalently, the intersection of their images is $(m-1)$-dimensional. We extend this adjacency relation on other conjugacy classes of finite-rank self-adjoint operators which leads to a natural generalization of Grassmann graphs. Let ${\mathcal C}$ be a conjugacy class formed by finite-rank self-adjoint operators with eigenspaces of dimension greater than $1$. Under the assumption that operators from ${\mathcal C}$ have at least three eigenvalues we prove that every automorphism of the corresponding generalized Grassmann graph is the composition of an automorphism induced by a unitary or anti-unitary operator and the automorphism obtained from a permutation of eigenspaces with the same dimensions. The case when the operators from ${\mathcal C}$ have two eigenvalues only is covered by classical Chow's theorem which says that there are graph automorphisms induced by semilinear automorphisms not preserving orthogonality.
