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2007.61: The hit problem for symmetric polynomials over the Steenrod algebra

2007.61: A. S. JANFADA and R. M. W. WOOD (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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DOI: 10.1017/S0305004102006059

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 2000 > 08 General algebraic systems
MIMS number:2007.61
Deposited By:Miss Louise Stait
Deposited On:03 April 2007

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