The Drinfeld realization of the elliptic quantum group B_{q,λ}(A_{2}^{(2)})
Abstract
We construct a realization of the Loperator satisfying the RLLrelation of the facetype elliptic quantum group B_{q,λ}(A2(2)). The construction is based on the elliptic analog of the Drinfeld currents of U_{q}(A2(2)), which forms the elliptic algebra U_{q,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 U_{q}(A2(2)) and a Heisenberg algebra. In the levelone 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}(A2(2))analog of the B_{q,λ}(A2(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 A2(2) face model.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 August 2004
 DOI:
 10.1063/1.1767296
 arXiv:
 arXiv:math/0401055
 Bibcode:
 2004JMP....45.3146K
 Keywords:

 02.20.Uw;
 02.20.Sv;
 Quantum groups;
 Lie algebras of Lie groups;
 Mathematics  Quantum Algebra;
 Mathematical Physics;
 17B37;
 81R50;
 82B23
 EPrint:
 40 pages