Mathematical Sciences: The Combinatoric Structure of Representations of Semi-Simple Groups Over Valued Fields

本研究属于群体表征理论领域。 首席研究员将开发一个代数谐波 半单表示论的变换分析 Hecke代数的表示理论。 本项目要考虑的中心问题是 Lusztig猜想指出，某些不变量附加 可以从多项式中计算。 这 是群论中的一个难点和中心问题。 它也有 在其他数学领域的影响。

This research is in the area of group representation theory. The principal investigator will develop an algebraic harmonic analysis to transfer the representation theory of semisimple groups to the representation theory of Hecke algebras. The central problem to be considered in this project is the Lusztig conjecture which states that certain invariants attached to an algebraic group can be calculated from polynomials. This is a difficult and central problem in group theory. It also has implications in other areas of mathematics.