Non-existence of negative derivations on the higher Nash blowup local algebra

Abstract: Let $f\in\mathbb{C}[x_1,\ldots,x_s]$ be a weighted homogeneous polynomial having an isolated singularity and $\mathcal{T}_n(f)$ be its higher Nash blowup local algebra. We show that $\mathcal{T}_n(f)$ does not admit negative weighted derivations for $n\geq2$. This answers affirmatively a conjecture of Hussain-Ma-Yau-Zuo.