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Universal R-matrix and functional relations

Herman Boos

Fachbereich C – Physik, Bergische Universität Wuppertal, 42097 Wuppertal, Germany

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Frank Göhmann

Fachbereich C – Physik, Bergische Universität Wuppertal, 42097 Wuppertal, Germany

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Andreas Klümper

Fachbereich C – Physik, Bergische Universität Wuppertal, 42097 Wuppertal, Germany

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Khazret S. Nirov

Institute for Nuclear Research of the Russian Academy of Sciences, 60th October Ave 7a, 117312 Moscow, Russia

Current address: Fachbereich C – Physik, Bergische Universität Wuppertal, 42097 Wuppertal, Germany.

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, and

Alexander V. Razumov

Institute for High Energy Physics, 142281 Protvino, Moscow Region, Russia

Current address: Max-Planck-Institut für Mathematik, Vivatsgasse, 7, 53111, Bonn, Germany.

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https://doi.org/10.1142/S0129055X14300052Cited by:19 (Source: Crossref)

Abstract

We collect and systematize general definitions and facts on the application of quantum groups to the construction of functional relations in the theory of integrable systems. As an example, we reconsider the case of the quantum group related to the six-vertex model. We prove the full set of the functional relations in the form independent of the representation of the quantum group in the quantum space and specialize them to the case of the six-vertex model.

Keywords:

AMSC: 17B37, 17B80, 81R50, 81R12, 16T25

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