The hit problem for symmetric polynomials over the Steenrod algebra

JANFADA, A. S. and WOOD, R. M. W. (2002) The hit problem for symmetric polynomials over the Steenrod algebra. Mathematical Proceedings of the Cambridge Philosophical Society, 133 (2). pp. 295-303. ISSN 0305-0041

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Abstract

We cite [18] for references to work on the hit problem for the polynomial algebra P(n) = [open face F]2[x1, ;…, xn] = [oplus B: plus sign in circle]d[gt-or-equal, slanted]0 Pd(n), viewed as a graded left module over the Steenrod algebra [script A] at the prime 2. The grading is by the homogeneous polynomials Pd(n) of degree d in the n variables x1, …, xn of grading 1. The present article investigates the hit problem for the [script A]-submodule of symmetric polynomials B(n) = P(n)[sum L: summation operator]n , where [sum L: summation operator]n denotes the symmetric group on n letters acting on the right of P(n). Among the main results is the symmetric version of the well-known Peterson conjecture. For a positive integer d, let [mu](d) denote the smallest value of k for which d = [sum L: summation operator]ki=1(2[lambda]i[minus sign]1), where [lambda]i [gt-or-equal, slanted] 0.

Item Type:	Article
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 08 General algebraic systems
Depositing User:	Ms Lucy van Russelt
Date Deposited:	03 Apr 2007
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/765

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