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arXiv · 2310.07215

Affine Springer Fibers and Generalized Haiman Ideals

Joshua P. Turner
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Abstract

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.

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Joshua P. Turner. 2024-07-25. Affine Springer Fibers and Generalized Haiman Ideals. https://doi.org/10.1093/imrn%2Frnae146

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