Quantum Groups and Functional Relations: A synthesis of methods for integrable systems

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We plan to intensify and extend our work on the mathematical structure ofquantum integrable and integrable stochastic systems associated with quantumloop algebras. We will develop methods for solving the spectral problem forthese classes of physical systems and for the exact calculation of theirthermodynamic quantities and correlation functions. The central tool to beused and further developed will be systems of functional equations such asTQ-equations, Q- and Y-systems, inversion relations and various types ofquantum Knizhnik-Zamolodchikov equations for the calculation of form factorsand correlation functions. We shall pay special attention to distinguishuniversal properties, based on the algebra, from physical properties, based onthe representation. The former are supposed to be sufficient for thederivation of the functional equations, the latter become important for thespecific solutions. Emphasis will be put on a generalization of existingfunctional equations to higher rank algebras and to systems associated withquantum loop algebras of series other than the A-type (the B-, C- andD-series). On the side of applications we plan to explore the applicability offunctional equations in the study of integrable stochastic systems.