The spherical harmonics \(Y^l(x)\) are functions defined on the sphere \(S^2\). They form a basis of the space on function on the sphere:
On this space it is nautal how the group \(O(3)\) acts, Given \(p_a, p_v\) two scalar representations:
\(L\) is representation of \(O(3)\). But \(L\) is not irreducible. It can be decomposed via a change of basis into a sum of irreps,
where the change of basis are the spherical harmonics!
As a consequence, the spherical harmonics are equivariant,
r = s2_grid()
r is a grid on the sphere.