Commutation relations of vertex operators related with the spin representation of $U_q(D_n^{(1)})$

Abstract

We calculate commutation relations of vertex operators for the spin representation of $U_q(D_n^{(1)})$ by using recursive formulae of R-matrices. In quantum symmetry approach, we obtain the energy and momentum spectrum of the quantum spin chain model related with the spin representation from these commutation relations.