The Drinfeld Realization of the Elliptic Quantum Group B_{q,lambda}(A_2^(2))

Abstract

We construct a realization of the L-operator satisfying the RLL-relation of the face type elliptic quantum group B_{q,lambda}(A_2^(2)). The construction is based on the elliptic analogue of the Drinfeld currents of U_q(A_2^(2)), which forms the elliptic algebra U_{q,p}(A_2^(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 U_q(A_2^(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 U_{q,p}(A_2^(2))-analogue of the B_{q,lambda}(A_2^(2)) -intertwining operators. The resultant operators coincide with those of the vertex operators in the dilute A_L model, which is known to be a RSOS restriction of the A_2^(2) face model.