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

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dc.creatorKonno, Hitoshi
dc.date2006-12-19
dc.date.accessioned2026-07-07T09:34:34Z
dc.date.available2026-07-07T09:34:34Z
dc.descriptionFor any affine Lie algebra ${\mathfrak g}$, we show that any finite dimensional representation of the universal dynamical $R$ matrix ${\cal R}(λ)$ of the elliptic quantum group ${\cal B}_{q,λ}({\mathfrak g})$ 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 ${\cal B}_{q,λ}({\mathfrak g})$ and the elliptic face (IRF or SOS) models. In particular, we construct vector representations of ${\cal R}(λ)$ 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.
dc.descriptionThis 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/
dc.identifierhttps://arxiv.org/abs/math/0612558
dc.identifierhttp://arxiv.org/abs/math/0612558
dc.identifierSIGMA 2 (2006), 091, 25 pages
dc.identifierdoi:10.3842/SIGMA.2006.091
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159536
dc.subjectQuantum Algebra
dc.subjectMathematical Physics
dc.subjectExactly Solvable and Integrable Systems
dc.titleDynamical R Matrices of Elliptic Quantum Groups and Connection Matrices for the q-KZ Equations
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