Representation theory in exactly solvable systems

精确可解系统中的表示论

• 批准号: FT180100099
• 负责人: Dr Ian Marquette
• 金额: $ 51.02万
• 依托单位: The University of Queensland
• 依托单位国家: 澳大利亚
• 项目类别: ARC Future Fellowships
• 财政年份: 2019
• 资助国家: 澳大利亚
• 起止时间: 2019-01-05 至 2024-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/FT180100099
• 关键词: Representation; theory; exactly; solvable; systems

This project aims to develop the representation theory of Lie and generalised Lie algebras related to exactly solvable models. The project will exploit several innovative ideas on the structure of quadratic algebras, Casimir invariants, differential operator realisations, roots systems, characters and indecomposable representations. This will give fundamental mathematical insight and allow the construction of new, exactly solvable models. This will have an impact on theoretical physics as exactly solvable models play a central role in our understanding of a plethora of physical phenomena.

本项目旨在发展与精确可解模型相关的李代数和广义李代数的表示理论。该项目将在二次代数的结构、Casimir不变量、微分算子实现、根系统、特征标和不可分解表示方面利用几个创新的想法。这将提供基本的数学洞察力，并允许构建新的、精确可解的模型。这将对理论物理产生影响，因为精确可解模型在我们理解过多的物理现象时发挥着核心作用。