Stable vector bundles on generalized Kummer varieties

For an abelian surface \(A\), we explicitly construct two new families of stable vector bundles on the generalized Kummer variety \(K_n(A)\) for \(n\geqslant 2\). The first is the family of tautological bundles associated to stable bundles on \(A\), and the second is the family of the "wrong-way" fibers of a universal family of stable bundles on the dual abelian surface \(\widehat{A}\) parametrized by \(K_n(A)\). Each family exhibits a smooth connected component in the moduli space of stable bundles on \(K_n(A)\), which is holomorphic symplectic but not simply connected, contrary to the case of K3 surfaces.