Modular character sheaves

模块化字符滑轮

• 批准号: DP170101579
• 负责人: Hon Prof Anthony Henderson
• 金额: $ 23.9万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2017
• 资助国家: 澳大利亚
• 起止时间: 2017-01-01 至 2021-06-30
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP170101579
• 关键词: Modular; character; sheaves

This project aims to complete the fundamental mathematical theory of modular group representations, the algebraic description of symmetry over finite number systems. Group representation theory can be applied to any linear problem involving symmetry. However, the modular case, where the characteristic of the underlying field is a prime number, is less understood than real or complex scalars, and this lack of understanding blocks potential applications. This project will use geometric methods to answer questions about modular representations of the finite groups of Lie type, the most important class of finite groups. This project could make modular representation theory essential for computations, enabling faster solutions to problems of linear algebra and allowing future applications in such areas as data transmission technology.

本项目旨在完成模群表示的基本数学理论，有限数系统上对称性的代数描述。群表示论可以应用于任何涉及对称性的线性问题。然而，模的情况下，其中的基础字段的特征是一个素数，是不太了解比真实的或复杂的标量，这种缺乏了解块潜在的应用。这个项目将使用几何方法来回答有关有限群的Lie型的模表示的问题，Lie型是有限群中最重要的一类。该项目可以使模块化表示理论对计算至关重要，从而更快地解决线性代数问题，并允许未来在数据传输技术等领域的应用。