Combinatorial and Representation Theoretic Methods in Number Theory

本项目旨在利用代数组合学的工具探索数论和表象理论之间的联系。重要的数论对象的对称性和构造，如Whittaker函数，是由李代数和根系的模型支撑的。该项目预计将推进建筑的代数框架。预期的结果包括这些对象的统一组合模型，以及结构向无限维环境的延伸。这将有利于数论的应用，并加强与数学物理的新生联系。

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.