On Two Families of Quantum Vertex Algebras of FRT-Type

Abstract

We consider two new families of quantum vertex algebras which are associated with the type A trigonometric R-matrix and elliptic R-matrix of the eight-vertex model. We show that their \(\phi \)-coordinated representation theory is governed by the so-called FRT-operator, h-adically restricted operator satisfying the FRT-relation, and we demonstrate some applications of this result. Finally, in the elliptic case, we investigate the properties of the quantum determinant associated with the corresponding quantum vertex algebra.