Affine Springer Fibers and Generalized Haiman Ideals
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929456531111936 |
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| author | Turner, Joshua P. |
| author_facet | Turner, Joshua P. |
| contents | We compute the Borel-Moore homology of unramified affine Springer fibers for $\mathrm{GL}_n$ under the assumption that they are equivariantly formal and relate them to certain ideals discussed by Haiman. For $n=3$, we give an explicit description of these ideals, compute their Hilbert series, generators and relations, and compare them to generalized $(q,t)$ Catalan numbers. We also compare the homology to the Khovanov-Rozansky homology of the associated link, and prove a version of a conjecture of Oblomkov, Rasmussen, and Shende in this case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_07215 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Affine Springer Fibers and Generalized Haiman Ideals Turner, Joshua P. Algebraic Geometry We compute the Borel-Moore homology of unramified affine Springer fibers for $\mathrm{GL}_n$ under the assumption that they are equivariantly formal and relate them to certain ideals discussed by Haiman. For $n=3$, we give an explicit description of these ideals, compute their Hilbert series, generators and relations, and compare them to generalized $(q,t)$ Catalan numbers. We also compare the homology to the Khovanov-Rozansky homology of the associated link, and prove a version of a conjecture of Oblomkov, Rasmussen, and Shende in this case. |
| title | Affine Springer Fibers and Generalized Haiman Ideals |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2310.07215 |