  With the use of a certain type of the Schwinger boson representation of the
su(4) algebra, the Bonn model for many-quark systems and an extension of the
model, in which the energies of the various exact states are controled, namely,
the energies are enhanced or de-enhanced, are investigated. Especially, the
triplet formation and the pairing correlation in many-quark states are
discussed. In the boson space, all the results are analytically expressed in
the exact forms.
