Zero-one dual characters of flagged Weyl modules
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911043496706048 |
|---|---|
| author | Guo, Peter L. Lin, Zhuowei Peng, Simon C. Y. |
| author_facet | Guo, Peter L. Lin, Zhuowei Peng, Simon C. Y. |
| contents | We prove a criterion of when the dual character $χ_{D}(x)$ 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 $χ_{D}(x)$ are either 0 or 1. This settles a conjecture proposed by M{é}sz{á}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{é}sz{á}ros--St. Dizier and Hodges--Yong, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_10933 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Zero-one dual characters of flagged Weyl modules Guo, Peter L. Lin, Zhuowei Peng, Simon C. Y. Combinatorics Algebraic Geometry Representation Theory 05E10, 05E14, 05A19, 14N15 We prove a criterion of when the dual character $χ_{D}(x)$ 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 $χ_{D}(x)$ are either 0 or 1. This settles a conjecture proposed by M{é}sz{á}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{é}sz{á}ros--St. Dizier and Hodges--Yong, respectively. |
| title | Zero-one dual characters of flagged Weyl modules |
| topic | Combinatorics Algebraic Geometry Representation Theory 05E10, 05E14, 05A19, 14N15 |
| url | https://arxiv.org/abs/2411.10933 |