Elliptic Quantum Group $U_{q,p} (B_{N}^{(1)})$ and Vertex Operators (String theory, integrable systems and representation theory)

Abstract

Assuming the existence of the L-operators, we study the Hopf algebroid structure of Uq, p(B(1) N). As an application, we derive the type I and II vertex operators, which intertwine the Uq, p(B(1) N)-modules of generic level, by assuming some analytic properties of the L-operators. For the level-1 case, we construct their free field realizations and show that the results satisfy the desired commutation relations with coefficients given by the elliptic dynamical R-matrices of the B(1) N type.