Generic representations of the finite general linear groups and the Steenrod algebra. I. (English) Zbl 0813.20049

Kuhn, Nicholas J.

Am. J. Math. 116, No. 2, 327-360 (1994).

This is the first in a series of three papers intended to develop the recent work about the Steenrod algebra as part of the representation theory of the general linear groups over finite fields. In the present paper the author introduces “generic representation theory” and then uses it to develop the Steenrod algebra. A generic embedding theorem is proved which, via a generalized Morita theorem, is then used to derive much of the “Sullivan conjecture algebra” in a unified way.

Reviewer: V.L.Popov (Ann Arbor)

MSC:

20G05	Representation theory for linear algebraic groups
55S10	Steenrod algebra
20G40	Linear algebraic groups over finite fields

Keywords:

additive category; abelian category; Sullivan conjecture algebra; Steenrod algebra; general linear groups over finite fields; generic embedding theorem; Morita theorem