Permutation symmetry for the tomographic probability distribution of a   system of identical particles
  The symmetry properties under permutation of tomograms representing the states of a system of identical particles are studied. Starting from the action of the permutation group on the density matrix we define its action on the tomographic probability distribution. Explicit calculations are performed in the case of the two-dimensional harmonic oscillator. 
V. I Man'ko, L. Rosa, P. Vitale