  On the basis of the formalism proposed by three of the present authors (A.K.,
J.P.and M.Y.), generalized Lipkin model consisting of (M+1) single-particle
levels is investigated. This model is essentially a kind of the
su(M+1)-algebraic model and, in contrast to the conventional treatment, the
case, where fermions are partially occupied in each level, is discussed. The
scheme for obtaining the orthogonal set for the irreducible representation is
presented.
