Abstract: By means of the basis functions with quasispin-symplectic symmetry and the method of constructing expose operator proved by Kummer,the extreme point problem of the N-repre-sentability theory of the reduced density matrix in quantum chemistry is studied Furthermore,on the basis of the former works,some more extreme points of the convex set of the second reduced density matrix are discovered.

Key words: Multi-body wavefunction, Symplectic symmetry, Reduced density matrix, N-representability problem