Elliptic algebra Uq;p(bsl2) : Drinfeld currents and vertex operators

We investigate the structure of the elliptic algebra Uq;p(bsl2) introduced earlier by one of the authors. Our construction is based on a new set of generating series in the quantum ane algebra Uq(bsl2), which are elliptic analogs of the Drinfeld currents. They enable us to identify Uq;p(bsl2) with the tensor product of Uq(bsl2) 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 Uq;p(bsl2) for the 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 eld representation. math.QA/9802002 (to appear in Communications in Mathematical Physics