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Hit Polynomials and the Canonical Antiautomorphism of the Steenrod Algebra

Judith H. Silverman
Proceedings of the American Mathematical Society
Vol. 123, No. 2 (Feb., 1995), pp. 627-637
DOI: 10.2307/2160923
Stable URL: http://www.jstor.org/stable/2160923
Page Count: 11
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Hit Polynomials and the Canonical Antiautomorphism of the Steenrod Algebra
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Abstract

In this paper, we generalize a formula of Davis (Proc. Amer. Math. Soc. 44 (1974), 235-236) for the antiautomorphism of the mod-2 Steenrod algebra A(2), in the process formulating the analogue of the Adem relations for products $Sq\overset{t - 1}{(\overbrace{0, \ldots, 0}, a) \cdot Sq\overset{t - 1}{\overbrace{0, \ldots, 0}, b)$. We also state a generalization of a conjecture by the author and Singer (On the action of Steenrod squares on polynomial algebras II, J. Pure Appl. Algebra (to appear)) concerning the A(2)-action on F2[ x1, ..., xs] and use the antiautomorphism formula to prove several cases of the generalized conjecture. We discuss the relationship between the two conjectures and make explicit a sufficient condition for Monks's work to prove a special case of the original conjecture. Finally, we illustrate in a table the relative strengths of the special cases of the conjectures known to be true.

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