From representations of the rational Cherednik algebra to parabolic
Hilbert schemes via the Dunkl-Opdam subalgebra
From representations of the rational Cherednik algebra to parabolic
Hilbert schemes via the Dunkl-Opdam subalgebra
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 …