On the action of the Steenrod algebra on the modular invariants of special linear group

TL;DR

This paper computes how the Steenrod algebra acts on the generators of the invariant algebra of the special linear group over finite fields, advancing understanding of algebraic topology and modular invariant theory.

Contribution

It provides explicit calculations of the Steenrod algebra action on invariants of SL(n, Z/p), a novel contribution to modular invariant theory.

Findings

Explicit formulas for Steenrod algebra action on SL(n, Z/p) invariants.

Enhanced understanding of algebraic structures in modular invariant theory.

Foundation for further algebraic topology research involving special linear groups.

Abstract

We compute the action of the Steenrod algebra on generators of algebras of invariants of special linear group ${SL_n=SL(n,\mathbb Z/p)}$ in the polynomial algebra with $ p$ an odd prime number.