Elliptic Quantum Group U_{q,p}(\hat{sl}_2) and 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,λ}(\hat{sl}_2). This shows a consistency of our H-Hopf algebroid structure even in the case with non-zero central element.

15 pages. Typos fixed. Version to appear in J.Phys.A :Math.and Theor., special issue on Recent Developments in Infinite Dimensional Algebras and Their Applications to Quantum Integrable Systems 2007

References in corpus (8)

• Solutions of the quantum dynamical Yang-Baxter equation and dynamical quantum groups
• Exchange dynamical quantum groups
• On representations of the elliptic quantum group $E_{\tau ,\eta }(s{l}_2)$
• Elliptic quantum groups $E_{\tau ,\eta }(s{l}_2)$ and quasi-Hopf algebras
• Elliptic algebra U_{q,p}(^sl_2): Drinfeld currents and vertex operators
• An Elliptic Algebra $U_{q,p}(\widehat{s{l}_2})$ and the Fusion RSOS Model
• The Vertex-Face Correspondence and Correlation Functions of the Fusion Eight-Vertex Model I: The General Formalism
• Elliptic U(2) quantum group and elliptic hypergeometric series

Cited by in corpus (5)

• Elliptic Quantum Group U_{q,p}(\hat{sl}_2), Hopf Algebroid Structure and Elliptic Hypergeometric Series
• Elliptic Deformed Superalgebra $u_{q,p}(\widehat{sl}(M|N))$
• Elliptic algebra, Frenkel-Kac construction and root of unity limit
• Elliptic Quantum Toroidal Algebras, Z-algebra Structure and Representations
• Wakimoto realization of the elliptic algebra $U_{q,p}(\widehat{s{l}_N})$