ALGEBRAIC COMBINATORICS

no. 1
Doubly transitive lines II: Almost simple symmetries
Iverson, Joseph W.1; Mixon, Dustin G.2
1 Department of Mathematics Iowa State University Ames IA
2 Department of Mathematics The Ohio State University Columbus OH
Algebraic Combinatorics, Volume 7 (2024) no. 1, pp. 37-76.

We study lines through the origin of finite-dimensional complex vector spaces that enjoy a doubly transitive automorphism group. This paper classifies those lines that exhibit almost simple symmetries. We introduce a general recipe involving Schur covers to recover doubly transitive lines from their automorphism group. Combining our results with recent work on the affine case by Dempwolff and Kantor [13], we deduce a classification of all linearly dependent doubly transitive lines in real or complex space.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.324
Classification: 52C35, 05E18, 20B25, 20B20
Keywords: equiangular lines, doubly transitive, roux, Higman pair, equiangular tight frame
Iverson, Joseph W. 1; Mixon, Dustin G. 2

1 Department of Mathematics Iowa State University Ames IA
2 Department of Mathematics The Ohio State University Columbus OH
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Iverson, Joseph W.; Mixon, Dustin G. Doubly transitive lines II:  Almost simple symmetries. Algebraic Combinatorics, Volume 7 (2024) no. 1, pp. 37-76. doi : 10.5802/alco.324. https://alco.centre-mersenne.org/articles/10.5802/alco.324/

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