  In some special zones of the high-dimensional coordinate space of few-body
systems with identical particles, the operation of an element (or a product of
elements) of the symmetry groups of the Hamiltonian on a quantum state might be
equivalent to the operation of another element. Making use of the matrix
representations of the groups, the equivalence leads to a set of homogeneous
linear equations imposing on the wave functions. When the matrix of these
equations is non-degenerate, the wave functions will appear as nodal surfaces
in these zones. In this case, these zones are prohibited. In this paper,
tightly bound 4-boson systems with three types of interaction have been studied
analytically and numerically. The existence of the universal prohibited zones
has been revealed, and their decisive effect on the structures of the
eigenstates is demonstrated.
