  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.
