N. Pavloff, DISCRETE SYMMETRIES IN THE WEYL EXPANSION FOR QUANTUM BILLIARDS, Journal of physics. A, mathematical and general, 27(12), 1994, pp. 4317-4323
We consider two- and three-dimensional quantum billiards with discrete
symmetries. The boundary condition is either Dirichlet or Neumann. We
derive the first terms of the Weyl expansion for the level density pr
ojected onto the irreducible representations of the symmetry group. Th
e formulae require only knowledge of the character table of the group
and the geometrical properties (such as surface, perimeter etc ... ) o
f sub-parts of the billiard invariant under a group transformation. As
an illustration, the method is applied to the icosahedral billiard.