  In order to calculate correlation functions of the chiral Potts model, one
only needs to study the eigenvectors of the superintegrable model. Here we
start this study by looking for eigenvectors of the transfer matrix of the
periodic tau_2(t)model which commutes with the chiral Potts transfer matrix. We
show that the degeneracy of the eigenspace of tau_2(t) in the Q=0 sector is
2^r, with r=(N-1)L/N when the size of the transfer matrix L is a multiple of N.
We introduce chiral Potts model operators, different from the more commonly
used generators of quantum group U-tilde_q(sl-hat(2)). From these we can form
the generators of a loop algebra L(sl(2)). For this algebra, we then use the
roots of the Drinfeld polynomial to give new explicit expressions for the
generators representing the loop algebra as the direct sum of r copies of the
simple algebra sl(2).
