Modular Representations of Finite Groups, Codes and Projective Geometry Over Finite Fields

有限域上有限群、代码和射影几何的模表示

• 批准号: 0071060
• 负责人: Peter K. Sin
• 金额: --
• 依托单位: University of Florida
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-07-01 至 2004-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0071060&HistoricalAwards=false
• 关键词: Modular; Representations; Finite; Groups; Codes

AbstractThe planned research lies at the junction of three areas, modular representations of finite groups, finite projective geometry and the theory of designs and their codes. Under this project, Sin will continue to develop a general framework in which techniques of representation theory and group cohomology can be applied to attack combinatorial problems about codes and geometries, at the same time studying how the latter areas may provide a more geometric viewpoint in representation theory. The successful outcome of this research should lead to further new methods and results in all three theories and speed the circulation of ideas among them.

摘要本计划的研究集中在有限群的模表示、有限射影几何和设计及其规范理论三个领域的交叉点上。在这个项目中，Sin将继续发展一个通用的框架，在这个框架中，表示理论和群上同调技术可以应用于攻击关于编码和几何的组合问题，同时研究后者如何在表示理论中提供更多的几何观点。这项研究的成功结果应该会导致这三种理论进一步的新方法和新结果，并加速它们之间的思想流通。