Mathematics – Algebraic Topology
Scientific paper
2009-03-28
Geom. Topol. Monogr. 11 (2007) 379-397
Mathematics
Algebraic Topology
This is the version published by Geometry & Topology Monographs on 14 November 2007
Scientific paper
10.2140/gtm.2007.11.379
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 how the semistandard Young tableaux can be used to index a set of monomials which span Q^d(n). The hook formula, which calculates the number of semistandard Young tableaux, then gives an upper bound for the dimension of Q^d(n). In the particular degree d where the Steinberg module appears for the first time in P(n) the upper bound is exact and Q^d(n) can then be identified with the Steinberg module.
Walker Grant
Wood R. M. W.
No associations
LandOfFree
Young tableaux and the Steenrod algebra does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Young tableaux and the Steenrod algebra, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Young tableaux and the Steenrod algebra will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-202122