Designs related through projective and Hopf maps

2023/10/18 by Ayodeji Lindblad, Lindblad, Ayodeji · 1 citation
Mathematics · #05B30 (primary) #41A55 #41A63 #52C35 #65D32 (secondary) #Algebraic and Geometric Analysis #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Mathematics and Applications #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2310.12091

openalex publication_date 2023/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We verify a construction which, for \Bbb K the reals, complex numbers, quaternions, or octonions, builds a spherical t-design by placing a spherical t-design on each \Bbb K-projective or \Bbb K-Hopf fiber associated to the points of a \lfloor t/2\rfloor-design on a quotient projective space \BbbKPⁿ≠\BbbOP² or sphere. This generalizes work of König and Kuperberg, who verified the \Bbb K=\Bbb C case of the projective settings, and of Okuda, who (inspired by independent observation of this construction by Cohn, Conway, Elkies, and Kumar) verified the \Bbb K=\Bbb C case of the generalized Hopf settings.

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• Asymptotically short generalizations of t-design curves

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