Zero-one dual characters of flagged Weyl modules

We prove a criterion of when the dual character χ D(x) of the flagged Weyl module associated a diagram D in the grid [n]× [n] is zero-one, that is, the coefficients of monomials in χ D(x) are either 0 or 1. This settles a conjecture proposed by Mészáros–St. Dizier–Tanjaya. Since Schubert polynomials and key polynomials occur as special cases of dual flagged Weyl characters, our approach provides a new and unified proof of known criteria for zero-one Schubert/key polynomials due to Fink–Mészáros–St. Dizier and Hodges–Yong, respectively.