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

Eugene Gorsky, José Simental, Monica Vazirani

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 $\mat…