The elliptic algebra U_{q,p}(\hat{sl}_N) and the Drinfeld realization of the elliptic quantum group B_{q,λ}(\hat{sl}_N)

Details 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 elliptic algebra U_{q,p}(\hat{sl}_N) and the Drinfeld realization of the elliptic quantum group B_{q,λ}(\hat{sl}_N)

2002-10-24

arxiv.org/abs/math/0210383v1

Commun.Math.Phys. 239 (2003) 405-447

Mathematics

Quantum Algebra

47 pages, Latex, No figures

Scientific paper

10.1007/s00220-003-0860-2

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

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