Capped Vertex Functions for $\text{Hilb}^n (\mathbb{C}^2)$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916684316540928 |
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| author | Ayers, Jeffrey Smirnov, Andrey |
| author_facet | Ayers, Jeffrey Smirnov, Andrey |
| contents | We obtain explicit formulas for capped descendent vertex functions of $\text{Hilb}^n(\mathbb{C}^2)$ for descendents given by the exterior algebra of the tautological bundle. This formula provides a one-parametric deformation of the generating function for normalized Macdonald polynomials. In particular, we show that the capped vertex functions are rational functions of the quantum parameter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_00498 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Capped Vertex Functions for $\text{Hilb}^n (\mathbb{C}^2)$ Ayers, Jeffrey Smirnov, Andrey Mathematical Physics High Energy Physics - Theory Algebraic Geometry Combinatorics Representation Theory We obtain explicit formulas for capped descendent vertex functions of $\text{Hilb}^n(\mathbb{C}^2)$ for descendents given by the exterior algebra of the tautological bundle. This formula provides a one-parametric deformation of the generating function for normalized Macdonald polynomials. In particular, we show that the capped vertex functions are rational functions of the quantum parameter. |
| title | Capped Vertex Functions for $\text{Hilb}^n (\mathbb{C}^2)$ |
| topic | Mathematical Physics High Energy Physics - Theory Algebraic Geometry Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2406.00498 |