Representations and invariants of algebraic groups

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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.