Canonical bases for standard modules of affine Hecke algebras

点击翻译按钮获取中文摘要

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.