Groupes quantiques associes aux courbes rationnelles et elliptiques et leurs applications
Groupes quantiques associes aux courbes rationnelles et elliptiques et leurs applications
摘要：
论文由作者在昂热大学（法国）答辩。全文共分四个部分。第一部分（法语）是介绍性的，并致力于量子群，可积系统和统计模型之间的关系。在第二部分（英文）的过渡函数的周期户田链解释的形式主义的合理的拉克斯运营商。在第三部分（法语）中，我们比较了两个椭圆量子群，并得出它们属于两个不同的双代数范畴的结论。第四部分（英文）包含了SOS模型的配分函数在椭圆量子群投影下的构造。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
