论文标题
简单表面奇点上点的希尔伯特（Hilbert
Euler numbers of Hilbert schemes of points on simple surface singularities and quantum dimensions of standard modules of quantum affine algebras
论文作者
论文摘要
我们证明了Arxiv中的Gyenge，Némethi和Szendrői的猜想：1512.06844，Arxiv：1512.06848提供了Eulers数量的Hilbert Shemes的生成函数的公式c^2/γ$，其中$γ$是$ \ mathrm {sl}（2）$的有限子组。我们从声称与$γ$ at $ζ= \ exp（\ frac {2πi} {2（h^\ vee+1）} $相关的量子仿射代数的标准模块的量子尺寸始终是$ 1 $，这是Kuniba [Kuniba [Kun93]的特殊情况。这里$ h^\ vee $是双coxeter号码。我们还证明了该索赔，该索赔以前不以$ e_7 $，$ e_8 $而闻名。
We prove the conjecture by Gyenge, Némethi and Szendrői in arXiv:1512.06844, arXiv:1512.06848 giving a formula of the generating function of Euler numbers of Hilbert schemes of points $\operatorname{Hilb}^n(\mathbb C^2/Γ)$ on a simple singularity $\mathbb C^2/Γ$, where $Γ$ is a finite subgroup of $\mathrm{SL}(2)$. We deduce it from the claim that quantum dimensions of standard modules for the quantum affine algebra associated with $Γ$ at $ζ= \exp(\frac{2πi}{2(h^\vee+1)})$ are always $1$, which is a special case of a conjecture by Kuniba [Kun93]. Here $h^\vee$ is the dual Coxeter number. We also prove the claim, which was not known for $E_7$, $E_8$ before.
