  Starting with an operator in the universal enveloping algebra of a
semi-simple, complex Lie group the nearest neighbor statistics of the spectra
of this operator along a sequence of representations are discussed.
  After a short introduction in chapter 1 this problem is motivated by a
general construction of the classical limit for quantum mechanical systems,
which is adopted to this setting, in chapter 2. In chapter 3 it is shown that
for simple operators, i.e., operators of the Lie algebra the nearest neighbor
statistics along a sequence of irreducible representations converge to the
Dirac measure. After a suitable completion of the universal enveloping algebra
the convergence to Poisson statistics is proved in chapter 4 for the
exponentials of generic operators. The proof makes use of a combinatorial
inequality of the Katz-Sarnak type for tori, which is proved in chapter 5. In
the appendix the necessary facts from group theory and the theory of nearest
neighbor distributions are gathered.
