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OPTIMAL LINE PACKINGS FROM FINITE GROUP ACTIONS

Part of: Permutation groups Representation theory of groups Circuits, networks Discrete geometry Nontrigonometric harmonic analysis

Published online by Cambridge University Press:  20 January 2020

JOSEPH W. IVERSON ,
JOHN JASPER  and
DUSTIN G. MIXON
JOSEPH W. IVERSON
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742, USA Department of Mathematics, Iowa State University, Ames, IA 50011, USA; jwi@iastate.edu
JOHN JASPER
Affiliation:
Department of Mathematics and Statistics, South Dakota State University, Brookings,SD 57007, USA; john.jasper@sdstate.edu
DUSTIN G. MIXON
Affiliation:
Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA; mixon.23@osu.edu

Abstract

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We provide a general program for finding nice arrangements of points in real or complex projective space from transitive actions of finite groups. In many cases, these arrangements are optimal in the sense of maximizing the minimum distance. We introduce our program in terms of general Schurian association schemes before focusing on the special case of Gelfand pairs. Notably, our program unifies a variety of existing packings with heretofore disparate constructions. In addition, we leverage our program to construct the first known infinite family of equiangular lines with Heisenberg symmetry.

MSC classification

Primary: 20B99: None of the above, but in this section 42C15: General harmonic expansions, frames 52C99: None of the above, but in this section
Secondary: 20C15: Ordinary representations and characters 94C30: Applications of design theory
Type
Discrete Mathematics
Information
Forum of Mathematics, Sigma , Volume 8 , 2020 , e6
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2020

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