Commutation relations of vertex operators related with the spin representation of Uq(Dn

Abstract

A new scheme to study the XXZ spin chain in massive regime is introduced by Davies et al in [1]. In this scheme, which is called symmetry approach, the space of states is identified with some Uq(A\_ ) -module. Under this identification, the XXZ Hamiltonian can be constructed on this module as an operator which commutes with the action of Uq(A '). Furthermore, the row transfer matrix and creation (annihilation) operators can be constructed by using vertex operators. In a similar way to [1], the higher spin chain [2] and the models related to the vector representation ofUq(A^) [3], Uq(B^ U q ( D ( n } ) [5] are studied. In this paper, we consider the model related with the spin representation of Uq(Dn ). In physics the model that we consider here is explained as follows. It is a one dimensional quantum spin chain model constructed from the spin representation of Uq(Dn )• The Hamiltonian acts on the space of the infinite tensor product