Abstract
Let GL n = GL(n,F p ) be the group of all n×ninvertible matrices over the field F p of p elements, p a prime number. As well known, a complete set of irreducible GL n -modules as submodules of the polynomial algebra was constructed by Stephen Doty and Grant Walker, Ton That Tri (see [1], [4]). Grant Walker has a conjecture that the occurence of these modules is the first occurence of these modules as submodules in the polynomial algebra. The aim of this paper is to give a proof of the above conjecture for p= 2.
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