Research objectives and content
The aim of this research project is to study the structure of the Steenrod algebra and its connections with representation theory. The structure of the Steenrod algebra is revealed to a large extent by its action on the cohomology of an elementary abelian p-group and it is by studying this action that. on one level. our goal is to be achieved. This cohomology ring has a natural action of the general linear group which interacts with that of the Steenrod algebra thus providing one example of the connections between the Steenrod algebra and representation theory that this project is concerned with. On another level, there is an equivalence between a category of generic' representations satisfying some finiteness condi- tions, and a quotient of the category of 'unstable' modules over the Steenrod algebra. This is a rather different example of the connections we are concerned with. which we aim to study in further detail. Training content (objective, benefit and expected impact)
The theory of unstable modules and the connection with 'generic' representations was largely developed by Lannes and Schwartz in Paris and Henn in Heidelberg. Therefore I anticipate that by spending time in Paris I will learn much on this subject from the first two authors as well as from likely visits by the third.