Algebraic & Geometric Topology 2 (2002) 563–590

DOI: 10.2140/agt.2002.2.563

arXiv: math.AT/0207213

Abstract

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(λ) of the full matrix semigroup M_n(F_p), the first occurrence of L(λ) as a composition factor in the polynomial algebra P=F_p[x₁, …, x_n] 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 A_p 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 A_p.

Keywords

Steenrod algebra, anti-automorphism, p–truncated polynomial algebra T, T–regular partition/representation

Mathematical Subject Classification

Primary: 55S10

Secondary: 20C20

References

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Publication

Received: 24 January 2002
Accepted: 10 July 2002
Published: 20 July 2002

Authors