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HIT POLYNOMIALS AND EXCESS IN THE MOD P STEENROD ALGEBRA

Published online by Cambridge University Press:  20 January 2009

Dagmar M. Meyer
Dagmar M. Meyer
Affiliation:
Laboratoire Analyse, Géométrie et Applications, Université Paris 13, 93430 Villetaneuse, France ([email protected])
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Abstract

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Let $p$ be an odd prime. The primary purpose of this paper is to determine the excess of the conjugates of the Steenrod operations $\mrm{P}[k;f]$, which are defined as $\mrm{P}[k;f]:=\mrm{P}(p^{k-1}f)\cdot\mrm{P}(p^{k-2}f)\cdot\cdots\cdot\mrm{P}(pf)\cdot\mrm{P}(f)$. The result is then used to obtain sufficient conditions for an element in the polynomial algebra $\mathbb{F}_p[x_1,\dots,x_s]$ to be in the image under the standard action of the Steenrod algebra. Results and methods are generalizations of previous work by Judith Silverman and by myself with Judith Silverman.

AMS 2000 Mathematics subject classification: Primary 55S10. Secondary 55S05

Keywords

hit polynomialsexcessSteenrod algebra
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 44 , Issue 2 , June 2001 , pp. 323 - 350
Copyright
Copyright © Edinburgh Mathematical Society 2001