Elliptic Quantum Group U_{q,p}(\hat{sl}_2) and Vertex Operators

TL;DR

This paper develops an H-Hopf algebroid framework for the elliptic quantum group U_{q,p}( ilde{sl}_2) and demonstrates that vertex operators as intertwining operators are consistent with previous quasi-Hopf algebra results.

Contribution

It introduces an H-Hopf algebroid structure to elliptic quantum groups and confirms the consistency of vertex operators with earlier quasi-Hopf algebra approaches.

Findings

Vertex operators coincide with previous quasi-Hopf algebra results.

H-Hopf algebroid structure remains consistent with non-zero central elements.

Provides a unified framework for elliptic quantum groups and their vertex operators.

Abstract

Introducing an H-Hopf algebroid structure into U_{q,p}(\widedhat{sl}_2), we investigate the vertex operators of the elliptic quantum group U_{q,p}(\widedhat{sl}_2) defined as intertwining operators of infinite dimensional U_{q,p}(\widedhat{sl}_2)-modules. We show that the vertex operators coincide with the previous results obtained indirectly by using the quasi-Hopf algebra B_{q,\lambda}(\hat{sl}_2). This shows a consistency of our H-Hopf algebroid structure even in the case with non-zero central element.