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.

该项目旨在利用代数组合学工具探索数论和表示论的联系。关键数论对象（例如 Whittaker 函数）的对称性和构造是以李代数和根系统模型为基础的。该项目预计将推进建筑的代数框架。预期结果包括这些对象的统一组合模型，以及将结构扩展到无限维度设置。这将有利于数论的应用，并加强与数学物理的新生联系。