Elliptic Quantum Group U_{q,p}(B_N^{(1)}) and Vertex Operators

TL;DR

This paper explores the algebraic structure of elliptic quantum groups U_{q,p}(B_N^{(1)}) and constructs vertex operators, providing explicit free field realizations and verifying their relations with elliptic dynamical R-matrices.

Contribution

It introduces the Hopf algebroid structure of U_{q,p}(B_N^{(1)}) and constructs vertex operators with free field realizations at level one.

Findings

Derived type I and II vertex operators for U_{q,p}(B_N^{(1)})

Constructed free field realizations satisfying elliptic dynamical R-matrix relations

Established the algebraic framework assuming L-operator existence

Abstract

Assuming the existence of the L-operators, we study the Hopf algebroid structure of U_{q,p}(B_N^{(1)}). As an application, we derive the type I and II vertex operators, which intertwine the U_{q,p}(B_N^{(1)})-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_N^{(1)} type.