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arXiv · 2308.10469

Upper bounds of dual flagged Weyl characters

Zhuowei Lin·Simon C. Y. Peng·Sophie C. C. Sun
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Abstract

For a subset $D$ of boxes in an $n\times n$ square grid, let $\chi_{D}(x)$ denote the dual character of the flagged Weyl module associated to $D$. It is known that $\chi_{D}(x)$ specifies to a Schubert polynomial (resp., a key polynomial) in the case when $D$ is the Rothe diagram of a permutation (resp., the skyline diagram of a composition). One can naturally define a lower and an upper bound of $\chi_{D}(x)$. M{\'e}sz{\'a}ros, St. Dizier and Tanjaya conjectured that $\chi_{D}(x)$ attains the upper bound if and only if $D$ avoids a certain subdiagram. We provide a proof of this conjecture.

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Zhuowei Lin, Simon C. Y. Peng, Sophie C. C. Sun. 2023-08-21. Upper bounds of dual flagged Weyl characters. https://arxiv.org/abs/2308.10469

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