This article is cited in 24 papers

Universal integrability objects

H. Boos^a, F. Gohmann^a, A. Klümper^a, Kh. Nirov^ba, A. V. Razumov<sup>cd

a</sup> University of Wuppertal
^b Institute for Nuclear Research, RAS, Moscow, Russia
^c Max-Planck-Institut für Mathematik, Bonn, Germany
^d Institute for High Energy Physics, Protvino, Moscow Oblast, Russia

Abstract: We discuss the main points of the quantum group approach in the theory of quantum integrable systems and illustrate them for the case of the quantum group $U_q(\mathcal L(\mathfrak{sl}_2))$. We give a complete set of the functional relations correcting inexactitudes in the previous considerations. We especially attend to the interrelation of the representations used to construct the universal transfer operators and $Q$-operators.

Keywords: integrable system, quantum group, representation, functional relation.

DOI: 10.4213/tmf8352

 English version: Theoretical and Mathematical Physics, 2013, 174:1, 21–39

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