Representations and invariants of algebraic groups

代数群的表示理论在特征0中得到了很好的理解，就像不变量理论中的许多问题一样。例如，使用特殊线性群的表示，可以完全描述它们在多项式环上的自然作用中的不变量。这个项目的目的是了解类似的结果，积极的特点。更确切地说，我们的目标是从G_2开始，得到正特征例外群的不变量理论基本定理。这些方法将涉及这些群体的代表性理论的详细理解，并将利用一种新的方法，使用诱导模块。

The representation theory of algebraic groups is well understood in characteristic 0, as are many problems from invariant theory. For example, using the representations of special linear groups, one can completely describe their invariants in natural actions on polynomial rings. The aim of this project is to understand analogous results in positive characteristic. More precisely,we aim to obtain the Fundamental Theorem of Invariant Theory for exceptional groups in positive characteristic, starting with G_2. The methods will involve a detailed understanding of the representation theory of these groups, and will utilise a novel approach using induced modules.