Elliptic algebra U_{q,p}(^sl_2): Drinfeld currents and vertex operators
Abstract
We investigate the structure of the elliptic algebra U_{q,p}(^sl_2) introduced earlier by one of the authors. Our construction is based on a new set of generating series in the quantum affine algebra U_q(^sl_2), which are elliptic analogs of the Drinfeld currents. They enable us to identify U_{q,p}(^sl_2) with the tensor product of U_q(^sl_2) and a Heisenberg algebra generated by P,Q with [Q,P]=1. In terms of these currents, we construct an L operator satisfying the dynamical RLL relation in the presence of the central element c. The vertex operators of Lukyanov and Pugai arise as `intertwiners' of U_{q,p}(^sl_2) for level one representation, in the sense to be elaborated on in the text. We also present vertex operators with higher level/spin in the free field representation.
Cite
@article{arxiv.math/9802002,
title = {Elliptic algebra U_{q,p}(^sl_2): Drinfeld currents and vertex operators},
author = {M. Jimbo and H. Konno and S. Odake and J. Shiraishi},
journal= {arXiv preprint arXiv:math/9802002},
year = {2012}
}
Comments
49 pages, (AMS-)LaTeX ; added an explanation of integration contours; added comments. To appear in Comm. Math. Phys. Numbering of equations is corrected