Spectral statistics along sequences of irreducible representations

Abstract

We discuss the nearest neighbor distribution of the eigenvalues for hermitian generators in the Lie algebra of a semisimple complex Lie Group along a sequence of irreducible representations. After the basic definitions a limit theorem for rays of irreducible representation is formulated. Then it is proved that only a certain kind of rescaling will give meaning full results in the general case. Finally, we give explicit formulas for the Lipkin operator in the case of SU(3).