Mathematical Sciences: Cohomology and Modular Representations of Algebraic Groups

本研究涉及代数群的表示理论。研究单连通半单代数群的非约化子群方案的不可分解有理内射模的结构。此外，还研究了这些内射模的Jantzen平移的结构及其与仿射Weyl群的Hecke代数的关系。本课题研究代数群的结构、上同调和表示。例如，这些代数群以线性变换群的形式出现。这是目前数学界的一个活跃领域。该项目将为解决特征p中的Lusztig猜想提供关键的一步。

This research is concerned with the representation theory of algebraic groups. The principal investigator will study the structure of the indecomposable rational injective modules for certain non-reduced subgroup schemes of a simply connected semisimple algebraic group. In addition, the structure of the Jantzen translations of these injective modules and the relationship between this structure and the Hecke algebra of the affine Weyl group will be studied. This project is concerned with the structure, cohomology and representations of algebraic groups. These algebraic groups occur, for example, as groups of linear transformations. This is an active area currently in mathematics. This project will provide a key step in solving the Lusztig conjecture in characteristic p.