  The Laplacian on the rotation group is invariant by conjugation. Hence, it
maps class functions to class functions. A maximal torus consists of block
diagonal matrices whose blocks are planar rotations. Class functions are
determined by their values of this maximal torus. Hence, the Laplacian induces
a second order operator on the maximal torus called the radial Laplacian. In
this paper, we derive the expression of the radial Laplacian. Then, we use it
to find the eigenvalues of the Laplacian, using that characters are class
functions whose expressions are given by the Weyl character formula. Although
this material is familiar to Lie-group experts, we gather it here in a
synthetic and accessible way which may be useful to non experts who need to
work with these concepts.
