Highly symmetric lines

Mikhail Ganzhinov

doi:10.1016/j.laa.2025.05.002

Highly symmetric lines

Mikhail Ganzhinov

Research output: Contribution to journal › Article › Scientific › peer-review

1 Citation (Scopus)

38 Downloads (Pure)

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.

Original language	English
Pages (from-to)	12-37
Number of pages	26
Journal	Linear Algebra and Its Applications
Volume	722
DOIs	https://doi.org/10.1016/j.laa.2025.05.002
Publication status	Published - 1 Oct 2025
MoE publication type	A1 Journal article-refereed

Keywords

Frames
Irreducible representations of finite groups
Line systems

Access to Document

10.1016/j.laa.2025.05.002Licence: CC BY

Highly_symmetric_linesFinal published version, 964 KBLicence: CC BY

Cite this

@article{bbbfd2638a5a4b01865d22635280d7bc,

title = "Highly symmetric lines",

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.",

keywords = "Frames, Irreducible representations of finite groups, Line systems",

author = "Mikhail Ganzhinov",

note = "Publisher Copyright: {\textcopyright} 2025 The Author",

year = "2025",

month = oct,

day = "1",

doi = "10.1016/j.laa.2025.05.002",

language = "English",

volume = "722",

pages = "12--37",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

publisher = "Elsevier",

}

TY - JOUR

T1 - Highly symmetric lines

AU - Ganzhinov, Mikhail

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 - https://www.scopus.com/pages/publications/105004938841

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 -

Highly symmetric lines

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this