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arXiv · 2411.10933

Zero-one dual characters of flagged Weyl modules

Peter L. Guo·Zhuowei Lin·Simon C. Y. Peng
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Abstract

We prove a criterion of when the dual character $\chi_{D}(x)$ of the flagged Weyl module associated to a diagram $D$ in the grid $[n]\times [n]$ is zero-one, that is, the coefficients of monomials in $\chi_{D}(x)$ are either 0 or 1. This settles a conjecture proposed by M{\'e}sz{\'a}ros--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--M{\'e}sz{\'a}ros--St. Dizier and Hodges--Yong, respectively.

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BibTeXRIS

Peter L. Guo, Zhuowei Lin, Simon C. Y. Peng. 2024-11-17. Zero-one dual characters of flagged Weyl modules. https://doi.org/10.4153/s0008414x2510120x

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