Combinatorial and Representation Theoretic Methods in Number Theory

数论中的组合和表示论方法

• 批准号: DE200101802
• 负责人: Dr Anna Puskas
• 金额: $ 20.02万
• 依托单位: The University of Queensland
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Early Career Researcher Award
• 财政年份: 2020
• 资助国家: 澳大利亚
• 起止时间: 2020-01-20 至 2022-10-02
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DE200101802
• 关键词: Combinatorial; Representation; Theoretic; Methods; Number

This Project aims to explore connections of Number Theory and Representation Theory by utilising tools of Algebraic Combinatorics. Symmetries and constructions of crucial number theoretic objects such as Whittaker functions are underpinned by models for Lie algebras and root systems. The Project expects to advance the algebraic framework of the constructions. Expected outcomes include a unified combinatorial model of these objects, and an extension of the costructions to the infinite dimensional setting. This will benefit the applications in Number Theory and strengthen nascent connections with Mathematical Physics.

该项目旨在通过使用代数组合学工具来探索数字理论和表示理论的联系。关键数字理论对象（例如Whittaker函数）的对称性和构造是由Lie代数和根系系统的模型支撑的。该项目预计将推进结构的代数框架。预期的结果包括这些对象的统一组合模型，以及将构造扩展到无限尺寸设置。这将受益于数量理论中的应用，并加强与数学物理学的新生联系。