Standard monomial theory modulo Frobenius in characteristic two
Abstract
Over a field of characteristic two, we develop a theory of standard monomials for polynomial rings modulo a Frobenius power of the maximal ideal generated by all variables. As a result, we obtain a filtration by modular GLn-representations whose characters are given by particular truncated Schur polynomials, thus proving a conjecture by Gao--Raicu--VandeBogert in the characteristic two case.
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