The Elliptic Algebra and the Drinfeld Realization of the Elliptic Quantum Group

摘要

By using the elliptic analogue of the Drinfeld currents in the elliptic algebra , we construct a L-operator, which satisfies the RLL-relations characterizing the face type elliptic quantum group . For this purpose, we introduce a set of new currents $K_j(v) (1leq jleq N)$ in . As in the N=2 case, we find a structure of as a certain tensor product of and a Heisenberg algebra. In the level-one representation, we give a free field realization of the currents in . Using the coalgebra structure of and the above tensor structure, we derive a free field realization of the -analogue of -intertwining operators. The resultant operators coincide with those of the vertex operators in the $A_{N-1}^{(1)}$ -type face model.