TY - JOUR
T1 - Highly symmetric lines
AU - Ganzhinov, Mikhail
N1 - Publisher Copyright:
© 2025 The Author
PY - 2025/10/1
Y1 - 2025/10/1
N2 - 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.
AB - 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.
KW - Frames
KW - Irreducible representations of finite groups
KW - Line systems
UR - http://www.scopus.com/inward/record.url?scp=105004938841&partnerID=8YFLogxK
U2 - 10.1016/j.laa.2025.05.002
DO - 10.1016/j.laa.2025.05.002
M3 - Article
AN - SCOPUS:105004938841
SN - 0024-3795
VL - 722
SP - 12
EP - 37
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
ER -