Linking first occurrence polynomials over Fp by Steenrod operations

This paper provides analogues of the results of [16] for odd primes p . It is proved that for certain irreducible representations L(λ) of the full matrix semigroup Mn(Fp), the first occurrence of L(λ) as a composition factor in the polynomial algebra P = Fp[x1, . . . , xn] is linked by a Steenrod operation to the first occurrence of L(λ) as a submodule in P. This operation is given explicitly as the image of an admissible monomial in the Steenrod algebra Ap under the canonical anti-automorphism χ . The first occurrences of both kinds are also linked to higher degree occurrences of L(λ) by elements of the Milnor basis of Ap . AMS Classification 55S10; 20C20