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- W2998990039 abstract "We prove the conjecture by Gyenge, N'emethi and SzendrH{o}i in arXiv:1512.06844, arXiv:1512.06848 giving a formula of the generating function of Euler numbers of Hilbert schemes of points $operatorname{Hilb}^n(mathbb C^2/Gamma)$ on a simple singularity $mathbb C^2/Gamma$, where $Gamma$ 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 $Gamma$ at $zeta = exp(frac{2pi i}{2(h^vee+1)})$ 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." @default.
- W2998990039 created "2020-01-23" @default.
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- W2998990039 date "2020-01-11" @default.
- W2998990039 modified "2023-09-30" @default.
- W2998990039 title "Euler numbers of Hilbert schemes of points on simple surface singularities and quantum dimensions of standard modules of quantum affine algebras" @default.
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- W2998990039 doi "https://doi.org/10.48550/arxiv.2001.03834" @default.
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