Over a field of characteristic zero, standard monomial theory and Young tableaux provide a connection between determinantal ideals of polynomial rings and irreducible representation theory of GL_n. In this talk, we present work towards developing an analogous theory over a field of characteristic two by working modulo a Frobenius power. As a result, we obtain modular GL_n-representations whose characters are given by particular truncated Schur polynomials, thus proving a conjecture by Gao-Raicu-VandeBogert in the characteristic two case. This is joint work with Laura Casabella.