Great antipodal sets on complex Grassmannian manifolds as designs with the smallest cardinalities
Great antipodal sets on complex Grassmannian manifolds as designs with the smallest cardinalities
复制标题
复杂格拉斯曼流形上的大对映集作为具有最小基数的设计
DOI：
10.1016/j.jalgebra.2020.05.004
复制
发表时间：
2020
影响因子：
0.9
通讯作者：
Okuda Takayuki
中科院分区：
文献类型：
--
作者：
Kurihara Hirotake;Okuda Takayuki
紧对称空间上的对映集是用点对称定义的。Chen-Nagano（1988）[10]在紧致对称空间中引入了一个不变的“2-数”作为对映集的最大基数，具有最大基数的对映集称为极大。Sánchez（1997）[34]和Tanaka-Tasaki（2013）[40]证明了在一个R-空间上的任何两个大对极集是同余的。特别地，复格拉斯曼流形上的大对极集在酉群的自然作用下是唯一的。本文的目的是给出复Grassmannian流形上的大对极集作为具有最小基数的某些设计的一个刻画。为此，我们扩展了Roy（2010）[31]引入的复格拉斯曼流形上的设计的定义。
Antipodal sets on compact symmetric spaces are defined in terms of point symmetries. Chen–Nagano (1988) [10] introduced an invariant “2-number” on compact symmetric spaces as the largest cardinalities of antipodal sets, and an antipodal set with the largest cardinality is said to begreat. Sánchez (1997) [34] and Tanaka–Tasaki (2013) [40] proved that any two great antipodal sets on a symmetricR-space are congruent. In particular, great antipodal sets on a complex Grassmannian manifold are unique up to the natural action of the unitary group. The aim of this paper is to give a characterization of great antipodal sets on complex Grassmannian manifolds as certain designs with the smallest cardinalities. To this, we extend the definition of designs on complex Grassmannian manifolds introduced by Roy (2010) [31].