Zero-one dual characters of flagged Weyl modules
Peter L. Guo, Zhuowei Lin, Simon C.Y. Peng

TL;DR
This paper characterizes when the dual character of flagged Weyl modules, including special cases like Schubert and key polynomials, has coefficients only 0 or 1, confirming a conjecture and unifying previous criteria.
Contribution
It provides a new criterion for zero-one dual characters of flagged Weyl modules, settling a conjecture and unifying existing results for Schubert and key polynomials.
Findings
Established a criterion for zero-one dual characters of flagged Weyl modules.
Unified proof for zero-one conditions of Schubert and key polynomials.
Confirmed a conjecture by M{é}sz{á}ros--St. Dizier--Tanjaya.
Abstract
We prove a criterion of when the dual character of the flagged Weyl module associated to a diagram in the grid is zero-one, that is, the coefficients of monomials in 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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Algebra and Geometry · Graph theory and applications · Finite Group Theory Research
