Dynamical R Matrices of Elliptic Quantum Groups and Connection Matrices for the q-KZ Equations

For any affine Lie algebra g, we show that any finite dimensional representation of the universal dynamical R matrix R(λ) of the elliptic quantum group Bq,λ(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,λ(g) and the elliptic face (IRF or SOS) models. In particular, we construct vector representations of R(λ) for g = A n , B (1) n , C (1) n , D (1) n , and show that they coincide with the face weights derived by Jimbo, Miwa and Okado. We hence confirm the conjecture by Frenkel and Reshetikhin.