Algebraic and Geometric Topology 2 (2002), paper no. 27, pages 563-590.

Linking first occurrence polynomials over F_p by Steenrod operations

Pham Anh Minh, Grant Walker

Abstract. This paper provides analogues of the results of [G.Walker and R.M.W. Wood, Linking first occurrence polynomials over F_2 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 M_n(F_p), the first occurrence of L(\lambda ) as a composition factor in the polynomial algebra P=F_p[x_1,...,x_n] 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 A_p 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 A_p.

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

AMS subject classification. Primary: 55S10. Secondary: 20C20.

DOI: 10.2140/agt.2002.2.563

E-print: arXiv:math.AT/0207213

Submitted: 24 January 2002. Accepted: 10 July 2002. Published: 20 July 2002.

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Pham Anh Minh, Grant Walker
Department of Mathematics, College of Sciences
University of Hue, Dai hoc Khoa hoc, Hue, Vietnam
Department of Mathematics, University of Manchester
Oxford Road, Manchester M13 9PL, U.K.

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