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This article is cited in 10 scientific papers (total in 10 papers)
Dynamical $R$ Matrices of Elliptic Quantum Groups and Connection Matrices for the $q$-KZ Equations
Hitoshi Konno Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8521, Japan
Abstract:
For any affine Lie algebra $\mathfrak g$, we show that any finite dimensional representation of the universal dynamical $R$ matrix $\mathcal R(\lambda)$ of the elliptic quantum group
$\mathcal B_{q,\lambda}(\mathfrak g)$ 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
$\mathcal B_{q,\lambda}(\mathfrak g)$ and the elliptic face (IRF or SOS) models. In particular, we construct vector representations of $\mathcal R(\lambda)$ 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.
Keywords:
elliptic quantum group; quasi-Hopf algebra.
Received: October 2, 2006; in final form November 28, 2006; Published online December 19, 2006
Citation:
Hitoshi Konno, “Dynamical $R$ Matrices of Elliptic Quantum Groups and Connection Matrices for the $q$-KZ Equations”, SIGMA, 2 (2006), 091, 25 pp.
Linking options:
https://www.mathnet.ru/eng/sigma119 https://www.mathnet.ru/eng/sigma/v2/p91
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