# Parabolic Hilbert schemes via the Dunkl-Opdam subalgebra

@article{Gorsky2020ParabolicHS, title={Parabolic Hilbert schemes via the Dunkl-Opdam subalgebra}, author={E. Gorsky and J. Simental and M. Vazirani}, journal={arXiv: Representation Theory}, year={2020} }

In this note we explicitly construct an action of the rational Cherednik algebra $H_{1,m/n}(S_n,\mathbb{C}^n)$ corresponding to the permutation representation of $S_n$ on the $\mathbb{C}^{*}$-equivariant homology of parabolic Hilbert schemes of points on the plane curve singularity $\{x^{m} = y^{n}\}$ for coprime $m$ and $n$. We use this to construct actions of quantized Gieseker algebras on parabolic Hilbert schemes on the same plane curve singularity, and actions of the Cherednik algebra at… Expand

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