Canonical bases for standard modules of affine Hecke algebras

仿射 Hecke 代数标准模的规范基

• 批准号: DP0344185
• 负责人: Hon Prof Anthony Henderson
• 金额: $ 16.22万
• 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: 2003
• 资助国家: 澳大利亚
• 起止时间: 2003-01-01 至 2006-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP0344185
• 关键词: Canonical; bases; standard; modules; affine

Lie theory is the study of a class of mathematical structures which arise in many different fields of mathematics, and in areas of physics such as quantum field theory. One such structure, much studied in the last twenty years, is the affine Hecke algebra of an algebraic group. These have standard modules (defined geometrically) which currently lack convenient bases (roughly speaking, ways to write them algebraically). The main aim of this project is to prove that standard modules have canonical bases with certain special properties, as conjectured by G. Lusztig.

李理论是对一类数学结构的研究，这些结构出现在许多不同的数学领域，以及物理领域，如量子场论。一种这样的结构是代数群的仿射Hecke代数，在过去的二十年里得到了大量的研究。它们有标准的模块(几何上定义的)，目前缺乏方便的基(粗略地说，用代数来写它们的方法)。正如G.Lusztig猜想的那样，这个项目的主要目的是证明标准模具有具有某些特殊性质的典范基。