Under numerical assumptions, connected components of moduli spaces of modular vector bundles on K3^{[n]}-type IHS manifolds are again IHS manifolds of K3^{[n]}-type and induce derived equivalences with the original manifolds.
Zhang, A twisted derived category of hyper-K\"ahler varieties of K3^ [n] -type , Preprint, arXiv:2502.02143 https://arxiv.org/pdf/2502.02143
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On moduli spaces of vector bundles on $K3^{[n]}$-type IHS manifolds
Under numerical assumptions, connected components of moduli spaces of modular vector bundles on K3^{[n]}-type IHS manifolds are again IHS manifolds of K3^{[n]}-type and induce derived equivalences with the original manifolds.