论文标题
高度对称线
Highly symmetric lines
论文作者
论文摘要
通过考虑框架向量的投射稳定剂，提出了高度对称框架的概括。这允许构建高度对称的线系统，并以更统一的方式研究高度对称的框架。高度对称线系统的构建涉及计算与有限基团相关的扭曲球形功能。进一步的概括包括高度对称的子空间系统。我们提供了几个示例，这些示例说明了我们的方法，包括3种新的接吻配置，这些配置在$ d = 10,11,14 $至510、592和1932的接吻号上提高了下限。
A generalization of highly symmetric frames is presented by considering also projective stabilizers of frame vectors. This allows construction of highly symmetric line systems and study of highly symmetric frames in a more unified manner. Construction of highly symmetric line systems involves computation of twisted spherical functions associated with finite groups. Further generalizations include definition of highly symmetric systems of subspaces. We give several examples which illustrate our approach including 3 new kissing configurations which improve lower bounds on the kissing number in $d=10,11,14$ to 510, 592 and 1932 respectively.
