On the application of Jucys-Murphy operators in the Hubbard model

The operator techniques based on the Jucys-Murphy operators were applied in the procedure of an immediate diagonalization of the one-dimensional Hubbard model. The Young orthogonal basis was given by the irreducible basis of the symmetric group acting on the set of nodes of the magnetic chain. The example of the attractive Hubbard model at the half-filled magnetic rings case was considered where the group $SU(2)\times SU(2)$ acts within the spin and pseudo-spin space. These techniques significantly reduced size of the eigenproblem of the Hubbard Hamiltonian.