Unramified affine Springer fibers and isospectral Hilbert schemes

@article{Kivinen2018UnramifiedAS,
  title={Unramified affine Springer fibers and isospectral Hilbert schemes},
  author={Oscar Kivinen},
  journal={arXiv: Algebraic Geometry},
  year={2018}
}
For any connected reductive group $G$ over $\mathbb{C}$, we revisit Goresky-Kottwitz-MacPherson's description of the torus equivariant Borel-Moore homology of affine Springer fibers $\mathrm{Sp}_\gamma\subset \mathrm{Gr}_G$, where $\gamma=at^d$, and $a$ is a regular semisimple element in the Lie algebra of $G$. In the case $G = GL_n$, we relate the equivariant cohomology of $\mathrm{Sp}_\gamma$ to Haiman's work on the isospectral Hilbert scheme of points on the plane. We also explain the… Expand
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