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 $\varphi$-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.

33 pages

References in corpus (6)

• Field Algebras
• On the quantum affine vertex algebra associated with trigonometric $R$-matrix
• Deforming vertex algebras by vertex bialgebras
• Quantum affine vertex algebras associated to untwisted quantum affinization algebras
• An approach to Quantum Conformal Algebra
• Yangian deformations of $\mathcal{S}$-commutative quantum vertex algebras and Bethe subalgebras