On the rigidity of some spherical 2-designs

概要

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In this note we shall determine which Mimura-type spherical 2-designs are rigid. Furthermore we show that spherical 2-designs of $ d + 2 $ points in $ \mathbf{S} ^{d-1} $ are rigid by showing the spherical 2-design of $ d + 2 $ points is unique. We also establish that a 2-design of $ d + 3 $ points is non-rigid. This work is intended to shed some lights on conjectures of Bannai. Bannai conjectured [Ba2] that there exists a function $ f(d, t) $ such that if $ X $ is a spherical $ t $-design in $ \mathbf{S} ^{d-1} $ and $ \mid X \mid > f(d,t) $, than $ X $ is non-rigid. He has showed that $ f(2,t) = 2t+1 $.
九州大学の論文