POWRE: Representations of Quantum Affine Algebras and Integrable Models

POWRE：量子仿射代数和可积模型的表示

• 批准号: 9870550
• 负责人: Rinat Kedem
• 金额: $ 7.5万
• 依托单位: University of Massachusetts Amherst
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-07-15 至 1999-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9870550&HistoricalAwards=false
• 关键词: POWRE; Representations; Quantum; Affine; Algebras

9870550 Kedem Integrable quantum field theories are related to certain integrable lattice models on the infinite lattice through the notion of the space of states, which carries the structure of an affine algebra representation. The PI will use the structure of representations of certain affine algebra's to define massive integrable field theories in terms of these representations. Previous results of the PI and co-authors suggest the existence of a certain fermionic construction of the coset representations of the Virasoro algebra corresponding to minimal models in conformal field theory and its deformations. This construction will reflect the role of the representation as the space of states of a particular massive deformation of a conformal field theory. The PI plans to apply results about the space of states of integrable lattice models to supply such a construction. This will give a representation theoretical proof of the fermionic character formulas. Kedem will use these results to find the representations corresponding to massive integrable models and its relation to non-critical RSOS models, and the role of deformed Virasoro algebra in such theories. In addition the PI will apply representation theoretical methods to find solutions to certain longstanding problems in the theory of lattice integrable models, associated with the chiral Potts model.

9870550 Kedem可积量子场理论通过态空间的概念与无限晶格上的某些可积晶格模型相联系，态空间具有仿射代数表示的结构。PI将使用某些仿射代数的表示的结构来根据这些表示定义大量的可积场理论。PI和合著者以前的结果表明，与共形场论中的极小模型相对应的Virasoro代数的陪集表示及其变形存在一定的费米子结构。这种结构将反映作为共形场论中特定大变形的态空间的表象的作用。PI计划应用关于可积格子模型的状态空间的结果来提供这样的构造。这将给出费米子特征标公式的表象理论证明。Kedem将利用这些结果找到对应于大规模可积模型的表示及其与非临界RSO模型的关系，以及变形Virasoro代数在此类理论中的作用。此外，PI将应用表示理论方法来寻找与手征Potts模型相关的格子可积模型理论中某些长期存在的问题的解决方案。