Harmonic analysis on Lie groups via hypergroup convolution structures

通过超群卷积结构对李群进行调和分析

• 批准号: ARC : DP0208556
• 负责人: Norman Wildberger
• 金额: $ 11万
• 依托单位: The University of New South Wales
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2002
• 资助国家: 澳大利亚
• 起止时间: 2002-01-01 至 2005-12-31
• 项目状态: 已结题
• 来源: https://researchdata.edu.au/harmonic-analysis-lie-convolution-structures/64659
• 关键词: Harmonic; analysis; Lie; groups; via

Harmonic analysis on Lie groups via hypergroup convolution structures. This project studies convolution structures for conjugacy classes\r\nof nilpotent and compact Lie groups and the connections with fusion rule algebras. The aims are to establish a suitable theory of almost periodic functions on a nilpotent Lie group to allow a\r\nwrapping theorem to be formulated, to describe precisely the\r\nclass hypergroup of a compact Lie group, and to clarify the relations of the latter with fusion rule algebras. This will result in further understanding of the Kirillov orbit method and the have applications to conformal field theory.

通过超群卷积结构对李群进行调和分析。该项目研究幂零和紧李群的共轭类的卷积结构以及与融合规则代数的联系。目的是建立一个合适的幂零李群上的几乎周期函数的理论，以允许制定包裹定理，精确描述紧李群的类超群，并阐明后者与融合规则代数的关系。这将导致对基里洛夫轨道方法的进一步理解及其在共形场理论中的应用。