Young tableaux and the Steenrod algebra
| dc.creator | Walker, Grant | |
| dc.creator | Wood, R M W | |
| dc.date | 2009-03-28 | |
| dc.date.accessioned | 2026-07-07T12:57:41Z | |
| dc.date.available | 2026-07-07T12:57:41Z | |
| dc.description | 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. | |
| dc.description | This is the version published by Geometry & Topology Monographs on 14 November 2007 | |
| dc.identifier | https://arxiv.org/abs/0903.5003 | |
| dc.identifier | http://arxiv.org/abs/0903.5003 | |
| dc.identifier | Geom. Topol. Monogr. 11 (2007) 379-397 | |
| dc.identifier | doi:10.2140/gtm.2007.11.379 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/225017 | |
| dc.subject | Algebraic Topology | |
| dc.subject | 55S10, 20C20 | |
| dc.title | Young tableaux and the Steenrod algebra | |
| dc.type | text |