  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.
