Infinite Dimensional Lie Algebras, Quantum Groups, and their Applications

主要研究人员：Nicolai Reshetikin提案编号：0307599机构：加州大学伯克利分校机构：无限维李代数、量子群及其应用本提案的主要主题是表示理论及其应用。在过去的几十年里，数学和物理之间的密切互动是数学与物理相互作用的重要特征。这一过程的很大一部分是在经典和量子可积系统的研究中开始的。这种相互作用导致了量子场论和弦理论在物理方面的革命性进展，以及几何、代数和拓扑学在数学方面的进步。这一建议的研究主要集中在这种相互作用产生的代数结构的研究以及这些结构的应用上。

Principal Investigator: Nicolai ReshetikhinProposal Number: 0307599Institution: University of California-BerkeleyABSTRACT: Infinite Dimensional Lie Algebras, Quantum Groups, and their ApplicationsThe main theme of this proposal is representation theory and its applications. The proposal is focused on the representation theory of quantum groups at roots of 1, on invariants of 3-manifolds with flat connections and related topological quantum field theories, on classical and quantum integrable systems, and on some solvable models of statistical mechanics.The last several decades have been characterized by an intense and productive interaction between mathematics and physics. A large part of this process was initiated in the study of classical and quantum integrable systems. This interaction has led to revolutionary progress in both quantum field theory and string theory on the physical side, and geometry, algebra and topology on the mathematical side. The research of this proposal is focused mostly on the study of algebraic structures resulting from this interaction and on applications of these structures.