Computing with Hecke algebras

使用赫克代数进行计算

• 批准号: 171106971
• 负责人: Professor Dr. Burkhard Külshammer
• 金额: --
• 依托单位: Lehrstuhl für Algebra und Zahlentheorie
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2010
• 资助国家: 德国
• 起止时间: 2009-12-31 至 2013-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/171106971?language=en
• 关键词: Computing; Hecke; algebras

Hecke algebras are a variety of structures playing a central role in algebra, in particular in the theory of finite groups and their representations. Here, we are interested in two classes of Hecke algebras: Iwahori-Hecke algebras and cyclotomic Hecke algebras, both of which are intimately connected to the representation theory of finite groups of Lie type. Motivated by theoretical questions concerning the structure and representation theory of these algebras, our aim is to develop new computational methods to handle Hecke algebras and their representations. To this end we will make combined use of techniques coming from various branches of computational mathematics, in particular from group theory and commutative algebra. These tools will then be applied to examine substantial interesting, but otherwise inaccessible examples, in order to collect data, to possibly detect previously unknown patterns, and thus to gain structural insights.

赫克代数是在代数中发挥核心作用的各种结构，特别是在有限群及其表示的理论中。在这里，我们对两类 Hecke 代数感兴趣：Iwahori-Hecke 代数和分圆 Hecke 代数，它们都与 Lie 型有限群的表示论密切相关。受有关这些代数的结构和表示论的理论问题的启发，我们的目标是开发新的计算方法来处理赫克代数及其表示。为此，我们将结合使用来自计算数学各个分支的技术，特别是来自群论和交换代数的技术。然后，这些工具将用于检查大量有趣但无法访问的示例，以便收集数据，可能检测以前未知的模式，从而获得结构见解。