  With the aim of applying to the Lipkin model in the case of open shell
system, a possible form of the boson realization for the su(2)-algebra is
proposed both in the Schwinger and the Holstein-Primakoff representation. The
basic idea is borrowed from the Schwinger boson realization for the
su(4)-algebra for many-quark system recently presented by the present authors.
As the simplest approximation, a certain approximate form is given and the
result is a natural generalization of the RPA result in the case of closed
shell system.
