Generic representations of orthogonal groups:the mixed functors

In 1993, Henn, Lannes and Schwartz established a very strong relation between the Steenrod algebra and the category F.p/ of functors from the category E of finite dimensional Fp –vector spaces to the category E of all Fp –vector spaces, where Fp is the prime field with p elements [5]. To be more precise, they study the category U of unstable modules over the Steenrod algebra localized away from the nilpotent unstable modules N i l ; they exhibit an equivalence between the quotient category U=N i l and a full subcategory of the category of functors F.p/. This equivalence is very useful and allows several important topological results to be derived from algebraic results in the category F.p/. For a recent interesting application of this equivalence to the cohomology of Eilenberg MacLane spaces, we refer the reader to the results obtained by Powell [9].