  We discuss a mapping procedure from a space of colorless three-quark clusters
into a space of elementary baryons and illustrate it in the context of a
three-color extension of the Lipkin model recently developed. Special attention
is addressed to the problem of the formation of unphysical states in the mapped
space. A correspondence is established between quark and baryon spaces and the
baryon image of a generic quark operator is defined both in its Hermitian and
non-Hermitian forms. Its spectrum (identical in the two cases) is found to
consist of a physical part containing the same eigenvalues of the quark
operator in the cluster space and an unphysical part consisting only of zero
eigenvalues. A physical subspace of the baryon space is also defined where the
latter eigenvalues are suppressed. The procedure discussed is quite general and
applications of it can be thought also in the correspondence between systems of
2n fermions and n bosons.
