Elliptic Algebra : Drinfeld Currents and Vertex Operators

Abstract:

We investigate the structure of the elliptic algebra introduced earlier by one of the authors. Our construction is based on a new set of generating series in the quantum affine algebra , which are elliptic analogs of the Drinfeld currents. They enable us to identify with the tensor product of 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 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.