New directions in Hecke algebras

赫克代数的新方向

• 批准号: DP200100712
• 负责人: A/Prof James Parkinson
• 金额: $ 31.81万
• 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: 2020
• 资助国家: 澳大利亚
• 起止时间: 2020-12-18 至 2024-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP200100712
• 关键词: New; directions; Hecke; algebras

To goal of this project is to make fundamental advances in representation theory, a powerful branch of mathematics focused on taking abstract mathematical structures and ``representing'' them in a concrete and useful way. In particular we aim to prove a series of long standing and influential conjectures by George Lusztig concerning the representation theory of Hecke algebras, objects which are ubiquitous in modern algebra. Our work will lead to new discoveries, a fundamentally deeper understanding of Kazhdan-Lusztig theory, and will drive future research. Benefits include enhanced international collaboration and increasing capacity in pure mathematics, especially in the cutting-edge area of representation theory.

该项目的目标是在表示论方面取得根本性进展，表示论是数学的一个强大分支，专注于采用抽象的数学结构并以具体且有用的方式“表示”它们。特别是，我们的目标是证明乔治·卢斯蒂格（George Lusztig）关于赫克代数表示论的一系列长期存在且有影响力的猜想，赫克代数是现代代数中普遍存在的对象。我们的工作将带来新的发现，从根本上更深入地理解 Kazhdan-Lusztig 理论，并将推动未来的研究。好处包括加强国际合作和提高纯数学能力，特别是在表示理论的前沿领域。