A Geometric Realization of Partially-Symmetric Macdonald Polynomials
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929542087573504 |
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| author | Goodberry, Ben Orr, Daniel |
| author_facet | Goodberry, Ben Orr, Daniel |
| contents | We formulate a precise conjecture relating integral form partially-symmetric Macdonald polynomials and the parabolic flag Hilbert schemes of Carlsson, Gorsky, and Mellit. This extends, in an explicit fashion, Haiman's realization of modified Macdonald symmetric functions via Hilbert schemes of points in the plane. As evidence for our conjecture we prove that it is compatible with the action of certain elements in Carlsson and Mellit's algebra $\mathbb{A}_{t,q}$, including degree $1$ Pieri formulas. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_11657 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Geometric Realization of Partially-Symmetric Macdonald Polynomials Goodberry, Ben Orr, Daniel Combinatorics Quantum Algebra Representation Theory 05E10, 05E05 We formulate a precise conjecture relating integral form partially-symmetric Macdonald polynomials and the parabolic flag Hilbert schemes of Carlsson, Gorsky, and Mellit. This extends, in an explicit fashion, Haiman's realization of modified Macdonald symmetric functions via Hilbert schemes of points in the plane. As evidence for our conjecture we prove that it is compatible with the action of certain elements in Carlsson and Mellit's algebra $\mathbb{A}_{t,q}$, including degree $1$ Pieri formulas. |
| title | A Geometric Realization of Partially-Symmetric Macdonald Polynomials |
| topic | Combinatorics Quantum Algebra Representation Theory 05E10, 05E05 |
| url | https://arxiv.org/abs/2312.11657 |