(p,q)-Sheaves and the Representability Problem
  General properties of new models of the electronic Fock spaces based on the notion of (p,q)-sheaves are studied. Interrelation between simple sheaves and density operators is established. Explicit expressions for the transformed reduced Hamiltonians in terms of the standard creation-annihilation operators are presented. General scheme of parametrization of p-electron states by k-electron means (k=2,3,...) is described and studied in detail for the case of sheaves induced by k-electron wavefunctions. It is demonstrated that under certain conditions p-electron problem may be reformulated as the eigenvalue problem in k-electron space equipped with certain p-electron metric. Simple numerical examples are given to illustrate our approach. 
A. I. Panin