Esoclinic subspaces, covers of the complete graph, and complex conference matrices
Document Type
Article
Publication Date
8-30-2024
Abstract
In 1992, Godsil and Hensel published a ground-breaking study of distance-regular antipodal covers of the complete graph that, among other things, introduced an important connection with equi-isoclinic subspaces. This connection seems to have been overlooked, as many of its immediate consequences have never been detailed in the literature. To correct this situation, we first describe how Godsil and Hensel's machine uses representation theory to construct equi-isoclinic tight fusion frames. Applying this machine to Mathon's construction produces ℝq+1 equi-isoclinic planes in Rq+1 for any even prime power q > 2. Despite being an application of the 30-year-old Godsil–Hensel result, infinitely many of these parameters have never been enunciated in the literature. Following ideas from Et-Taoui, we then investigate a fruitful interplay with complex symmetric conference matrices.
DOI
10.1016/j.laa.2024.08.002 ; arxiv:2212.12617
Source Publication
Linear Algebra and Its Applications (ISSN 0024-3795 | e-ISSN 1873-1856)
Recommended Citation
Fickus, M., Iverson, J. W., Jasper, J., & Mixon, D. G. (2024). Equi-isoclinic subspaces, covers of the complete graph, and complex conference matrices. Linear Algebra and Its Applications, 702, 240–249. https://doi.org/10.1016/j.laa.2024.08.002
arXiv:2212.12617 [math.CO]
Comments
The "Link to Full Text" on this page opens the arXiv.org preprint version of the article, hosted at the arXiv repository.
This article is scheduled to appear in the December 2024 issue of Linear Algebra and Its Applications as a subscription-access article. Elsevier published the article fully online before that issue, as cited below.