A diagram technique for nonorthogonal electron group functions. I. Right coset decomposition of symmetric group

For an N-electron system partitioned into a set of electron groups, an expanded arrow diagram (EAD) technique is proposed. It is useful when the wave function of the system is approximated by an antisymmetrized product of mutually nonorthogonal group functions. The technique provides a graphic representation of the right (left) coset decomposition of the symmetric group S_N with respect to its subgroup S_o generated by all the intragroup permutations. The connection between the EADs and arrow diagrams of Matsen, Klein et al., and Wilson is stated and used to prove the validity of the arrow diagram representation of the double coset decomposition of S_N with respect to S_o, as well as to obtain the decomposition coefficients explicitly. The technique is applicable to systems composed of any finite or infinite number of electron groups each containing an arbitrary number of electrons.