Number conserving mappings of shell-model algebras with SU(3) subalgebras

A special closed set of commutation relations satisfied by the fermion pair and multipole operators for a major shell in LST coupling is found. The case of the neutron (proton) p-shell with the structure SO(7) contains SU(3) is studied in detail. An exact Dyson mapping is constructed, which is subsequently hermitized. The method is directly applicable to the s-d shell which has structure SO(13)containsSU(6)containsSU(3). For higher shells, where the 3-dimensional harmonic oscillator SU(3) symmetry is destroyed by strong spin-orbit interaction, the experimentally plausible pseudo-SU(3) symmetry makes the method applicable