Temperley-Lieb Immanants of Ribbon Decomposition Matrices
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917548994330624 |
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| author | Nguyen, Son Pylyavskyy, Pavlo |
| author_facet | Nguyen, Son Pylyavskyy, Pavlo |
| contents | Ribbon decomposition matrices give determinantal formulas for skew Schur functions that include as special cases the classical Jacobi-Trudi, Giambelli, and Lascoux-Pragacz formulas. We prove that certain elements of Lusztig's dual canonical basis, called Temperley-Lieb immanants, are Schur-positive when evaluated on ribbon decomposition matrices. We conjecture that this positivity holds for all elements of the dual canonical basis. This is known in the special case of Jacobi-Trudi matrices by a result of Haiman. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12880 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Temperley-Lieb Immanants of Ribbon Decomposition Matrices Nguyen, Son Pylyavskyy, Pavlo Combinatorics Representation Theory Ribbon decomposition matrices give determinantal formulas for skew Schur functions that include as special cases the classical Jacobi-Trudi, Giambelli, and Lascoux-Pragacz formulas. We prove that certain elements of Lusztig's dual canonical basis, called Temperley-Lieb immanants, are Schur-positive when evaluated on ribbon decomposition matrices. We conjecture that this positivity holds for all elements of the dual canonical basis. This is known in the special case of Jacobi-Trudi matrices by a result of Haiman. |
| title | Temperley-Lieb Immanants of Ribbon Decomposition Matrices |
| topic | Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2605.12880 |