Linking first occurrence polynomials over Fₚ by Steenrod operations

الأصل · EN

This paper provides analogues of the results of [G.Walker and R.M.W. Wood, Linking first occurrence polynomials over F₂ by Steenrod operations, J. Algebra 246 (2001), 739--760] for odd primes p. It is proved that for certain irreducible representations L(lambda) of the full matrix semigroup Mₙ(Fₚ), the first occurrence of L(lambda) as a composition factor in the polynomial algebra P=Fₚ[x₁,...,xₙ] is linked by a Steenrod operation to the first occurrence of L(lambda) 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 chi. The first occurrences of both kinds are also linked to higher degree occurrences of L(lambda) by elements of the Milnor basis of Aₚ.