On the minimal power of $q$ in a Kazhdan-Lusztig polynomial
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866912055942971392 |
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| author | Gaetz, Christian Gao, Yibo |
| author_facet | Gaetz, Christian Gao, Yibo |
| contents | For $w$ in the symmetric group, we provide an exact formula for the smallest positive power $q^{h(w)}$ appearing in the Kazhdan-Lusztig polynomial $P_{e,w}(q)$. We also provide a tight upper bound on $h(w)$ in simply-laced types, resolving a conjecture of Billey-Postnikov from 2002. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_13695 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the minimal power of $q$ in a Kazhdan-Lusztig polynomial Gaetz, Christian Gao, Yibo Combinatorics Representation Theory For $w$ in the symmetric group, we provide an exact formula for the smallest positive power $q^{h(w)}$ appearing in the Kazhdan-Lusztig polynomial $P_{e,w}(q)$. We also provide a tight upper bound on $h(w)$ in simply-laced types, resolving a conjecture of Billey-Postnikov from 2002. |
| title | On the minimal power of $q$ in a Kazhdan-Lusztig polynomial |
| topic | Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2303.13695 |