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

本研究属于群表征理论领域。主要研究人员将发展一种代数调和分析，将半单群的表示理论转化为Hecke代数的表示理论。在这个项目中要考虑的中心问题是Lusztig猜想，该猜想指出附加到代数群上的某些不变量可以从多项式中计算出来。这是群论中的一个难点和中心问题。它对数学的其他领域也有影响。

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.