| Summary: | For any affine Lie algebra ${mathfrak g}$, we show that any finite dimensional representation of the universal dynamical $R$ matrix ${cal R}(lambda)$ of the elliptic quantum group ${cal B}_{q,lambda}({mathfrak g})$ coincides with a corresponding connection matrix for the solutions of the $q$-KZ equation associated with $U_q({mathfrak g})$. This provides a general connection between ${cal B}_{q,lambda}({mathfrak g})$ and the elliptic face (IRF or SOS) models. In particular, we construct vector representations of ${cal R}(lambda)$ for ${mathfrak g}=A_n^{(1)}$, $B_n^{(1)}$, $C_n^{(1)}$, $D_n^{(1)}$, and show that they coincide with the face weights derived by Jimbo, Miwa and Okado. We hence confirm the conjecture by Frenkel and Reshetikhin.
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