Spherical 7-Designs in 2
n
-Dimensional Euclidean Space |
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Authors: | VM Sidelnikov |
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Institution: | (1) Dept. of Mathematics and Mechanics, Moscow State University, Moscow, Russia |
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Abstract: | We consider a finite subgroup
n
of the group O(N) of orthogonal matrices, where N = 2
n
, n = 1, 2 .... This group was defined in 7]. We use it in this paper to construct spherical designs in 2
n
-dimensional Euclidean space R
N
. We prove that representations of the group
n
on spaces of harmonic polynomials of degrees 1, 2 and 3 are irreducible. This and the earlier results 1–3] imply that the orbit
n,2
x
t
of any initial point x on the sphere S
N – 1 is a 7-design in the Euclidean space of dimension 2
n
. |
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Keywords: | spherical design orthogonal matrix Euclidian space |
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