Schur positivity of the nabla operator on two-column modified Hall--Littlewood polynomials
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918513813225472 |
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| author | Qu, Menghao |
| author_facet | Qu, Menghao |
| contents | In this paper, we investigate the Schur positivity of modified Hall--Littlewood polynomials indexed by two-column partitions under the action of the $\nabla$ operator. Specifically, we resolve two conjectures posed by Bergeron, Garsia, Haiman, and Tesler in the two-column case. Furthermore, our approach demonstrates that these results can be extended to arbitrary powers $\nabla^k$ for all integers $k\geq 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_20954 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Schur positivity of the nabla operator on two-column modified Hall--Littlewood polynomials Qu, Menghao Combinatorics In this paper, we investigate the Schur positivity of modified Hall--Littlewood polynomials indexed by two-column partitions under the action of the $\nabla$ operator. Specifically, we resolve two conjectures posed by Bergeron, Garsia, Haiman, and Tesler in the two-column case. Furthermore, our approach demonstrates that these results can be extended to arbitrary powers $\nabla^k$ for all integers $k\geq 1$. |
| title | Schur positivity of the nabla operator on two-column modified Hall--Littlewood polynomials |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2605.20954 |