The Steenrod algebra action on generators of rings of invariants of subgroups of 𝐺𝐿_{𝑛}(𝑍/𝑝𝑍)

Abstract

We compute the action of the Steenrod algebra on rings of invariants of certain subgroups of GL n ( Z / p Z ) {\operatorname {GL} _n}({\mathbf {Z}}/p{\mathbf {Z}}) , namely, the upper triangular and parabolic subgroups. As a consequence we get the action on the Dickson algebra for any prime p p . The methods we use are elementary.