The elliptic algebra Uq,p((sl)over-capN) and the Drinfeld realization of the elliptic quantum group βq,λ ((sl)over-capN)

By using the elliptic analogue of the Drinfeld currents in the elliptic algebra U-q,U-p((sl) over cap (N)), we construct a L-operator, which satisfies the RLL-relations characterizing the face type elliptic quantum group B-q,B-lambda ((sl) over cap (N)). For this purpose, we introduce a set of new currents K-j (v) (1 less than or equal to j less than or equal to N) in U-q,U-p((sl) over cap (N)). As in the N = 2 case, we find a structure Of U-q,U-p((sl) over cap (N)) as a certain tensor product of B-q,B-lambda((sl) over cap (N)) and a Heisenberg algebra. In the level-one representation, we give a free field realization of the currents in U-q.p((sl) over cap (N)). Using the coalgebra structure of B-q,B-lambda((sl) over cap (N)) and the above tensor structure, we derive a free field realization of the U-q,U-p ((sl) over cap (N)) -analogue of B-q,B-lambda ((sl) over cap (N))-intertwining operators. The resultant operators coincide with those of the vertex operators in the A(N-1)((1))-type face model.