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Symmetry, Integrability and Geometry: Methods and Applications, 2006, Volume 2, 091, 25 pp.
DOI: https://doi.org/10.3842/SIGMA.2006.091
(Mi sigma119)
 

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
References:
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
Bibliographic databases:
Document Type: Article
MSC: 33D15; 81R50; 82B23
Language: English
Citation: Hitoshi Konno, “Dynamical $R$ Matrices of Elliptic Quantum Groups and Connection Matrices for the $q$-KZ Equations”, SIGMA, 2 (2006), 091, 25 pp.
Citation in format AMSBIB
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\by Hitoshi Konno
\paper Dynamical $R$~Matrices of Elliptic Quantum Groups and Connection Matrices for the $q$-KZ Equations
\jour SIGMA
\yr 2006
\vol 2
\papernumber 091
\totalpages 25
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  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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