Stratified bundles on the Hilbert Scheme of n points

Let k be an algebraically closed field of characteristic \(p > 3\) $p>3$ and S be a smooth projective surface over k with k-rational point x. For \(n \ge 2\) $n\ge 2$ , let \(S^{[n]}\) $S^{[n]}$ denote the Hilbert scheme of n points on S. In this note, we compute the fundamental group scheme \(\pi ^{\text {alg}}(S^{[n]}, {\tilde{nx}})\) ${\pi }^{\text{alg}}(S^{[n]},\widetilde{\mathit{nx}})$ defined by the Tannakian category of stratified bundles on \(S^{[n]}\) $S^{[n]}$ .