论文标题
从理性的Cherednik代数的代表到通过Dunkl-Opdam Subegra的抛物线希尔伯特计划
From representations of the rational Cherednik algebra to parabolic Hilbert schemes via the Dunkl-Opdam subalgebra
论文作者
论文摘要
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} \} $用于coprime $ m $和$ n $。我们使用它来构建量等的Gieseker代数在同一平面曲线奇异性上的抛物线式希尔伯特计划上的动作，以及Cherednik代数在$ t = 0 $上的动作在抛物线抛物性Hilbert Shemes上的等效性Hilbert Shemes在非降低的曲线curve $ \ \ \ \ \ \ \ \ \ \ {y^n} = 0 = $ contair obsiatiation = 0 $ contair的同源性上。通过dunkl-opdam元素产生的亚级数的理性Cherednik代数。
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 $t = 0$ on the equivariant homology of parabolic Hilbert schemes on the non-reduced curve $\{y^{n} = 0\}.$ Our main tool is the study of the combinatorial representation theory of the rational Cherednik algebra via the subalgebra generated by Dunkl-Opdam elements.
