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

量子群和函数关系：可积系统方法的综合

• 批准号: 429711968
• 负责人: Professor Dr. Andreas Kluemper
• 金额: --
• 依托单位: Fakultät für Mathematik und Naturwissenschaften
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/429711968?language=en
• 关键词: Quantum; Groups; Functional; Relations; synthesis

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.

我们计划加强和扩展我们的工作的数学结构的量子可积和可积随机系统与量子圈代数。我们将发展解决这些物理系统的光谱问题的方法，以及精确计算它们的热力学量和相关函数的方法。中心工具将被使用和进一步发展的系统的功能方程，如TQ方程，Q-和Y-系统，反演关系和各种类型的量子Knizhnik-Zamolodchikov方程计算的形状因子和相关函数。我们将特别注意基于代数、基于物理性质、基于表象的泛在性质。前者对于函数方程的推导是充分的，后者对于特解的求解是重要的。重点将放在推广现有的功能方程，以更高的秩代数和系统与量子回路代数系列以外的A型（B-，C-和D-系列）。在应用方面，我们计划探索函数方程在可积随机系统研究中的适用性。