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.

40 pages

References in corpus (4)

• The elliptic algebra U_{q,p}(\hat{sl}_N) and the Drinfeld realization of the elliptic quantum group B_{q,λ}(\hat{sl}_N)
• The twisted quantum affine algebra $U_q(A^{(2)_2)$ and correlation functions of the Izergin-Korepin model
• The Elliptic Algebra U_{q,p}(sl_N^) and the Deformation of W_N Algebra
• Quantum Knizhnik-Zamolodchikov equation associated with $U_q(A_2^{(2)})$ for $|q|=1$

Cited by in corpus (4)

• Elliptic Quantum Group U_{q,p}(\hat{sl}_2), Hopf Algebroid Structure and Elliptic Hypergeometric Series
• Elliptic Deformed Superalgebra $u_{q,p}(\widehat{sl}(M|N))$
• Algebraic Bethe ansatz for the elliptic quantum group $E_{\tau ,\eta }(A_2^{(2)})$
• Commutation relations of vertex operators for $U_q(\widehat{sl}(M|N))$