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Elliptic algebra U_{q,p}(^sl_2): Drinfeld currents and vertex operators

M. Jimbo·H. Konno·S. Odake·J. Shiraishi
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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.

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M. Jimbo, H. Konno, S. Odake, J. Shiraishi. 1998-01-31. Elliptic algebra U_{q,p}(^sl_2): Drinfeld currents and vertex operators. https://doi.org/10.1007/s002200050514

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