Algebraic groups and Springer theory

代数群和施普林格理论

• 批准号: DE160100975
• 负责人: A/Prof Ting Xue
• 金额: $ 21.55万
• 依托单位: The University of Melbourne
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Early Career Researcher Award
• 财政年份: 2016
• 资助国家: 澳大利亚
• 起止时间: 2016-06-30 至 2019-06-30
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DE160100975
• 关键词: Algebraic; groups; Springer; theory

This project aims to explore representation theory, which is a study of the basic symmetries that occur in nature. By its nature, representation theory has applications to number theory, physics, national security and internet security, and other sciences. Generalised Springer theory plays an important role in representations of finite groups of Lie type. The project aims to develop an analogous theory in a more general setting that includes symmetric spaces. Moreover, the project aims to address various outstanding problems in algebraic groups. The project also plans to explore the connection between the geometry of certain null-cones and deformations of Galois representations.

这个项目的目的是探索表征理论，这是一个研究自然界中发生的基本对称性。就其本质而言，表示论可以应用于数论、物理学、国家安全和互联网安全以及其他科学。广义施普林格理论在李型有限群的表示中起着重要作用。该项目的目的是在更一般的环境中开发一个类似的理论，包括对称空间。此外，该项目旨在解决代数群中的各种悬而未决的问题。该项目还计划探索某些零锥的几何形状与伽罗瓦表示的变形之间的联系。