Geodesic
Spherical 7-designs in $2^n$-dimensional Euclidean space
Journal of Algebraic Combinatorics, Tome 10 (1999) no. 3, pp. 279-288.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We consider a finite subgroup $THgr_{ n }$ of the group $O(N)$ of orthogonal matrices, where N = $2 ^{ n }$, n = 1, $2 \dots $. 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 $THgr_{ n }$ on spaces of harmonic polynomials of degrees 1, 2 and 3 are irreducible. This and the earlier results [1-3] imply that the orbit $THgr_{ n,2}$ x $^{ t }$ of any initial point x on the sphere S $_{ N - 1}$ is a 7-design in the Euclidean space of dimension $2 ^{ n }$.
Keywords: spherical design, orthogonal matrix, euclidian space 
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     author = {Sidelnikov, V.M.},
     title = {Spherical 7-designs in $2^n$-dimensional {Euclidean} space},
     journal = {Journal of Algebraic Combinatorics},
     pages = {279--288},
     publisher = {mathdoc},
     volume = {10},
     number = {3},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_1999__10_3_a0/}
}
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Sidelnikov, V.M. Spherical 7-designs in $2^n$-dimensional Euclidean space. Journal of Algebraic Combinatorics, Tome 10 (1999) no. 3, pp. 279-288. http://geodesic.mathdoc.fr/item/JAC_1999__10_3_a0/