A possible framework of the Lipkin model obeying the SU(n) algebra in arbitrary fermion number. I: The SU(2) algebras extended from the conventional fermion pair and determination of the minimum weight states

The minimum weight states of the Lipkin model consisting of n single-particle levels and obeying the SU(n) algebra are investigated systematically. The basic idea is to use the SU(2) algebra, which is independent of the SU(n) algebra. This idea has already been presented by the present authors in the case of the conventional Lipkin model consisting of two single-particle levels and obeying the SU(2) algebra. If this idea is followed, the minimum weight states are determined for any fermion number appropriately occupying n single-particle levels. Naturally, the conventional minimum weight state is included: all fermions occupy energetically the lowest single-particle level in the absence of interaction. The cases n = 2, 3, 4, and 5 are discussed in some detail.