Linking First Occurrence Polynomials over 2 by Steenrod Operations

It is proved that for every irreducible representation L(λ) of the full matrix semigroup Mn( 2), the first occurrence of L(λ) as a composition factor in the polynomial algebra P = 2[x1, …, xn] is linked by a Steenrod operation to the first occurrence of L(λ) as a submodule in P. This Steenrod operation is given explicitly as the image of an admissible monomial in the Steenrod squares Sqr under the canonical anti-automorphism χ of the mod 2 Steenrod algebra . The first occurrences of both kinds are also linked to higher degree occurrences of L(λ) by elements of the Milnor basis of .