The Drinfeld realization of the elliptic quantum group Bq,λ(A2(2))

Abstract

We construct a realization of the L-operator satisfying the RLL-relation of the face-type elliptic quantum group Bq,λ(A2(2)). The construction is based on the elliptic analog of the Drinfeld currents of Uq(A2(2)), which forms the elliptic algebra Uq,p(A2(2)). We give a realization of the elliptic currents E(z), F(z), and K(z) as a tensor product of the Drinfeld currents of Uq(A2(2)) and a Heisenberg algebra. In the level-one representation, we also give a free field realization of the elliptic currents. Applying these results, we derive a free field realization of the Uq,p(A2(2))-analog of the Bq,λ(A2(2))-intertwining operators. The resultant operators coincide with those of the vertex operators in the dilute AL model, which is known to be a RSOS restriction of the A2(2) face model.