Elliptic algebra Uq,p((sl)over-cap2):: Drinfeld currents and vertex operators

We investigate the structure of the elliptic algebra U-q,U-p((sl)over-cap(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)over-cap(2)), which are elliptic analogs of the Drinfeld currents. They enable us to identify U-q,U-p((sl)over-cap(2)) with the tensor product of U-q((sl)over-cap(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,U-p((sl)over-cap(2)) 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 field representation.