LetGLn=GL(n,Fp) be the group of alln×ninvertible matrices over the fieldFpof p elements, p a prime number. As well known, a complete set of irreducibleGLn-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 forp= 2.