Mathematical Sciences: Representations of Affine Hecke Algebras and Quantum Groups

该奖项支持仿射Hecke代数和量子群的表示理论的研究。 主要研究者将致力于完成半单分裂p-adic群的非分歧表示的分类，通过分级Hecke代数和等变同调。 他还将继续研究的参数空间，这些表示从角度来看，交叉上同调。 此外，他将研究规范基地包络代数和总的积极性在还原组的现实。 许多不同的代数对象可以表示为其他代数对象的变换的代数集合。 通过这些表征，可以确定它们的结构。 这个项目是关于某些代数的表示理论。 对这些代数的研究在整个数学和数学物理中都有应用。

This award supports research on the representation theory of affine Hecke algebras and quantum groups. The principal investigator will work on completing the classification of the unramified representations of semisimple split p-adic groups, via graded Hecke algebras and equivariant homology. He will also continue the study of the parameter space of these representations from the point of view of intersection cohomology. Further, he will study canonical bases in enveloping algebras and the total positivity in reductive groups over the reals. Many different algebraic objects can be represented as algebraic sets of transformations of other algebraic objects. Through these representations their structure can be determined. This project is concerned with the representation theory of certain algebras. The study of these algebras has applications throughout mathematics and mathematical physics.