Results on stability of tautological sheaves on Hilbert schemes of points are extended to higher dimensions and to the restriction of tautological sheaves to generalised Kummer varieties. This provides a big class of new examples of stable sheaves on higher dimensional irreducible symplectic manifolds. Some aspects of deformations of tautological sheaves are studied.
"Tautological sheaves: Stability, moduli spaces and restrictions to generalised Kummer varieties." Osaka J. Math. 53 (4) 889 - 910, October 2016.