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Young tableaux and the Steenrod algebra

2007
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Geometry and Topology Monographs
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unpublished

The purpose of this paper is to forge a direct link between the hit problem for the action of the Steenrod algebra A on the polynomial algebra P(n)=F_2[x_1,...,x_n], over the field F_2 of two elements, and semistandard Young tableaux as they apply to the modular representation theory of the general linear group GL(n,F_2). The cohits Q^d(n)=P^d(n)/P^d(n)\cap A^+(P(n)) form a modular representation of GL(n,F_2) and the hit problem is to analyze this module. In certain generic degrees d we show

doi:10.2140/gtm.2007.11.379
fatcat:bez27yps6rcwfnkhib7bvbo5km