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Mathematics > Functional Analysis

arXiv:2207.08266 (math)
[Submitted on 17 Jul 2022]

Title:Highly symmetric lines

Authors:Mikhail Ganzhinov
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Abstract: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.
Subjects: Functional Analysis (math.FA); Combinatorics (math.CO); Metric Geometry (math.MG)
Cite as: arXiv:2207.08266 [math.FA]
  (or arXiv:2207.08266v1 [math.FA] for this version)
  https://doi.org/10.48550/arXiv.2207.08266

Submission history

From: Mikhail Ganzhinov [view email]
[v1] Sun, 17 Jul 2022 19:27:10 UTC (20 KB)
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