An analogue of the Kostant-Rallis multiplicity theorem for   $\theta$-group harmonics
  The main result in this paper is the generalization of the Kostant-Rallis multiplicity formula to general {\theta}--groups (in the sense of Vinberg). The special cases of the two most interesting examples one for $E_6$ (three qubits) and one for $E_8$ are given explicit formulas. 
Nolan R. Wallach
math.RT