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September 10, 2025

Zero-one dual characters of flagged Weyl modules

Key Points

The study establishes when the dual character of flagged Weyl modules is zero-one, indicating coefficients are strictly 0 or 1.
A new criterion is proven, confirming a conjecture by Mészáros–St. Dizier–Tanjaya regarding dual flagged Weyl characters.
This approach also provides a unified proof for known criteria of zero-one Schubert and key polynomials.
Results clarify relationships between different polynomial types, possibly enhancing combinatorial applications.

Abstract

Abstract We prove a criterion of when the dual character ₃ (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 ₃ (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.

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