On last years "Darstellungstheorietag" Gordon James gave a lecture explaining, how to attach to each standard tableau t, whose shape is a 2-part partition \lambda of an natural naumber n, a polynomial p_t(x) with integer coefficients and p_t(q) many basis elements of the Specht module S(\lambda,q) of the general linear group GL(n,q) definded over the field with q elements (q = prime power). These basis elements are defined over any field in which the integer q is invertible. It is shown that we get indeed by this way a complete basis of the corresponding Specht module S(\lambda,q). Taking q to 1 one obtains (for 2-part partitions) a q-analogue for the well known theorem that an integral basis of the Specht S(\lambda,1) modules for symmetric groups S_n is labelled by standard \lambda tableaux.