Tesler identities for wreath Macdonald polynomials
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909618586779648 |
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| author | Romero, Marino Wen, Joshua Jeishing |
| author_facet | Romero, Marino Wen, Joshua Jeishing |
| contents | We give an explicit formula for an operator that sends a wreath Macdonald polynomial to the delta function at a character associated to its partition. This allows us to prove many new results for wreath Macdonald polynomials, especially pertaining to reciprocity: Macdonald--Koornwinder duality, evaluation formulas, etc. Additionally, we initiate the study of wreath interpolation Macdonald polynomials, derive a plethystic formula for wreath $(q,t)$-Kostka coefficients, and present series solutions to the bispectral problem involving wreath Macdonald operators. Our approach is to use the eigenoperators for wreath Macdonald polynomials that have been produced from quantum toroidal and shuffle algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01732 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tesler identities for wreath Macdonald polynomials Romero, Marino Wen, Joshua Jeishing Quantum Algebra Combinatorics Representation Theory Primary: 05E05, 81R10, Secondary: 33D52, 81R12 We give an explicit formula for an operator that sends a wreath Macdonald polynomial to the delta function at a character associated to its partition. This allows us to prove many new results for wreath Macdonald polynomials, especially pertaining to reciprocity: Macdonald--Koornwinder duality, evaluation formulas, etc. Additionally, we initiate the study of wreath interpolation Macdonald polynomials, derive a plethystic formula for wreath $(q,t)$-Kostka coefficients, and present series solutions to the bispectral problem involving wreath Macdonald operators. Our approach is to use the eigenoperators for wreath Macdonald polynomials that have been produced from quantum toroidal and shuffle algebras. |
| title | Tesler identities for wreath Macdonald polynomials |
| topic | Quantum Algebra Combinatorics Representation Theory Primary: 05E05, 81R10, Secondary: 33D52, 81R12 |
| url | https://arxiv.org/abs/2505.01732 |