Dynamical R Matrices of Elliptic Quantum Groups and Connection Matrices for the q-KZ Equations
Abstract
For any affine Lie algebra g, we show that any finite dimensional representation of the universal dynamical R matrix R(l) of the elliptic quantum group Bq,l(g) coincides with a corresponding connection matrix for the solutions of the q-KZ equation associated with Uq(g). This provides a general connection between Bq,l(g) and the elliptic face (IRF or SOS) models. In particular, we construct vector representations of R(l) for g = An(1), Bn(1), Cn(1), Dn(1), and show that they coincide with the face weights derived by Jimbo, Miwa and Okado. We h!
ence confirm the conjecture by Frenkel and Reshetikhin.- Publication:
-
SIGMA
- Pub Date:
- December 2006
- DOI:
- arXiv:
- arXiv:math/0612558
- Bibcode:
- 2006SIGMA...2..091K
- Keywords:
-
- elliptic quantum group;
- quasi-Hopf algebra;
- Mathematics - Quantum Algebra;
- Mathematical Physics;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- This is a contribution to the Proc. of the O'Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (June 2006, Budapest, Hungary), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/