New elements of the dual cone of the set of fermion N-representable 2-density
operators are proposed. So far, the explicit form of the corresponding
necessary conditions for N-representability is obtained for N=3. In this case
the new condition is stronger than the known B- and C-conditions for
3-representability. The results provide evidence that in the spectral
decomposition of the N-representable 2-density operator there exists an
intrinsic relation between the eigenvalue and the corresponding eigenfunction.
keywords: fermion N-representability problem, conditions for N-representability