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

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

2008-02-25

arxiv.org/abs/0802.3630v2

J.Phys.A41:194012,2008

Mathematics

Quantum Algebra

15 pages. Typos fixed. Version to appear in J.Phys.A :Math.and Theor., special issue on Recent Developments in Infinite Dimens

Scientific paper

10.1088/1751-8113/41/19/194012

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.

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