A. Silantyev
Published 2009-01-20Version 1
The thesis was defended by the author in University of Angers (France). It consists of four parts. The fist part (in French) is introductory and is devoted to relation between quantum groups, integrable systems and statistical models. In the second part (in English) the transition function of the periodic Toda chain is interpreted in terms of the formalism of rational Lax operators. In the third part (in French) one compares two elliptic quantum groups and one conclude that they belong to two different bialgebra categories. The fourth part (in English) contains a construction of the partition function of the SOS model in terms of the projections of an elliptic quantum group.
Comments: PhD thesis. Languages: French, English
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