one represents the hopping between nearest dimers (($y,z$)-plane) and between different dimer planes (see Fig. 1).

The equivalent form of the Hubbard Hamiltonian (4) is especially suitable because we can apply in the following the exact solution of the dimer problem (5). In the next step we express the construction operators $%
a_{\sigma}$ ($a_{\sigma}^{+}$) as linear combinations of the transition operators between different dimer states. This, in turn, allows to find the exact dimer representation of the whole Hamiltonian (4). The space of the dimer eigenvectors consists, however, of two subspaces. One of them corresponds to the lowest lying energy levels, the second one contains the levels with energies which in the large $U$ limit take on large, positive values. These levels in a reasonable temperature range cannot be occupied by electrons and therefore we can exclude them from further considerations. It is interesting to note that this approch, without any additional assumptions, applied to the dimer Hamiltonian (5) produces the analogy of the well known $t-J$ model (cf Refs \[31\], \[32\]). A similar approach can be applied to the Hamiltonian (4), describing the crystal as a whole. By eliminating from the considerations the unoccupied dimer energy levels in the 