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Highly symmetric lines.

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Title: Highly symmetric lines.
Authors: Ganzhinov, Mikhail1 (AUTHOR) mikhail.ganzhinov@aalto.fi
Source: Linear Algebra & its Applications. Oct2025, Vol. 722, p12-37. 26p.
Subjects: Finite groups, Spherical functions, Generalization, Kissing, Definitions
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. [ABSTRACT FROM AUTHOR]
Copyright of Linear Algebra & its Applications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 185778680
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: 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. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Linear Algebra & its Applications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1016/j.laa.2025.05.002
    Languages:
      – Code: eng
        Text: English
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      Pagination:
        PageCount: 26
        StartPage: 12
    Subjects:
      – SubjectFull: Finite groups
        Type: general
      – SubjectFull: Spherical functions
        Type: general
      – SubjectFull: Generalization
        Type: general
      – SubjectFull: Kissing
        Type: general
      – SubjectFull: Definitions
        Type: general
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      – TitleFull: Highly symmetric lines.
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            NameFull: Ganzhinov, Mikhail
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            – D: 01
              M: 10
              Text: Oct2025
              Type: published
              Y: 2025
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              Value: 722
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            – TitleFull: Linear Algebra & its Applications
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