Abstract
Based on representations of the symmetric group SN , an explicit and exact Schrodinger equation is derived for the U = ∞ Hubbard model in any dimcnsions with arbitrary number of holes, which clearly shows that during the movement of holes the spin background of electrons plays an important role. Starting from this, at T = 0 we have analysed the behaviour of the system depending on the dimensionality and number of holes. Based on the presented formalism, thermodynamic auantities have also been expressed using a loop summation technique in which the partition function is given in terms of characters of SN. In the case of the finite systems studied, the loop summation have been taken into account exactly up to the fourteenth order in reciprocal temperature and the results were corrected to a higher order based on Monte Carlo simulations. The results obtained suggest that the presented formalism increases the efficiency of the Monte Carlo simulations as well, because the spin part contribution of the background is automatically taken into account by the characters of SN.