un 2 00 7 Spherical harmonics and the icosahedron Nigel Hitchin
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چکیده
Spherical harmonics of degree l are the functions on the unit 2-sphere which satisfy ∆f = l(l + 1)f for the Laplace-Beltrami operator ∆. They form an irreducible representation of SO(3) of dimension 2l + 1 and are the restrictions to the sphere of homogeneous polynomials f(x1, x2, x3) of degree l which solve Laplace’s equation in R. This paper concerns a curious relationship between the case l = 3 and the regular icosahedron.
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تاریخ انتشار 2008