The Lipkin Model in the su(M+1)-Algebra for Many-Fermion System and its   Counterpart in the Schwinger Boson Representation
  Following the Schwinger boson representation for the su(M+1)- and the su(N,1)-algebra presented by two of the present authors (J. da P. and M. Y.) and Kuriyama, a possible counterpart of the Lipkin model in the su(M+1)-algebra formulated in the fermion space is presented. The free vacuum, which plays a fundamental role in the conventional treatment of the Lipkin model, is generalized in a quite natural way, and further, the excited state generating operators such as the particle-hole pairs are also given in a natural scheme. As concrete examples, the cases of the su(2)-, su(3)- and the su(4)-algebra are discussed. Especially, the case of the su(4)-algebra is investigated in detail in relation to the nucleon pairing correlations and the high temperature superconductivity. 
C.Providencia (Univ. de Coimbra, Portugal), J.da Providencia (Univ. de   Coimbra, Portugal), Y.Tsue (Kochi Univ., Japan), M....