Canonical bases for standard modules of affine Hecke algebras

李理论是一类数学结构的研究，出现在许多不同的数学领域，并在物理学领域，如量子场论。在过去的二十年里，人们对这样一种结构进行了大量的研究，这就是代数群的仿射Hecke代数。这些都有标准的模块（几何定义），目前缺乏方便的基础（粗略地说，方法来写他们的代数）。本项目的主要目的是证明标准模存在具有某些特殊性质的标准基，如G。卢斯蒂格

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.