Abstract:
In the paper we suggest an algorithm for calculation of the Laplace operator spectrum for real-valued and complex-valued functions defined on a connected compact simple Lie group with a bi-invariant Riemannian metric. By means of the algorithm an explicit calculation of the spectrum is given for all connected compact simple Lie groups of rank one and two.
Keywords:Laplace operator, spectrum, Lie group representation, highest weight, Killing form.