Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
The Invariants of the Clifford Groups
Designs, Codes and Cryptography
Spherical designs and finite group representations (some results of E. Bannai)
European Journal of Combinatorics - Special issue on algebraic combinatorics: in memory of J.J. Seidel
Spherical 5-designs obtained from finite unitary groups
European Journal of Combinatorics - Special issue on algebraic combinatorics: in memory of J.J. Seidel
A survey on spherical designs and algebraic combinatorics on spheres
European Journal of Combinatorics
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We consider a finite subgroup Θ_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 in2^n-dimensional Euclidean space R. We prove thatrepresentations of the group Θ_n on spaces of harmonicpolynomials of degrees 1, 2 and 3 are irreducible. This and theearlier results [1–3] imply that the orbit Θ_n, 2x of anyinitial point x on the sphere S_N − 1 is a 7-design in the Euclidean space of dimension 2^n.