On combinatorial invariance of parabolic Kazhdan-Lusztig polynomials
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866918043429371904 |
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| author | Barkley, Grant T. Gaetz, Christian |
| author_facet | Barkley, Grant T. Gaetz, Christian |
| contents | We show that the Combinatorial Invariance Conjecture for Kazhdan-Lusztig polynomials due to Lusztig and to Dyer, its parabolic analog due to Marietti, and a refined parabolic version that we introduce, are equivalent. We use this to give a new proof of Marietti's conjecture in the case of lower Bruhat intervals and to prove several new cases of the parabolic conjectures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04246 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On combinatorial invariance of parabolic Kazhdan-Lusztig polynomials Barkley, Grant T. Gaetz, Christian Combinatorics Representation Theory We show that the Combinatorial Invariance Conjecture for Kazhdan-Lusztig polynomials due to Lusztig and to Dyer, its parabolic analog due to Marietti, and a refined parabolic version that we introduce, are equivalent. We use this to give a new proof of Marietti's conjecture in the case of lower Bruhat intervals and to prove several new cases of the parabolic conjectures. |
| title | On combinatorial invariance of parabolic Kazhdan-Lusztig polynomials |
| topic | Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2404.04246 |