In this note we interpret a recent result of Gaberdiel et al [7] in terms of derived equivalences of K3 surfaces. We prove that there is a natural bijection between subgroups of the Conway group Co_0 with invariant lattice of rank at least four and groups of symplectic derived equivalences of D~b(X) of projective K3 surfaces fixing a stability condition. As an application we prove that every such subgroup G ? Co_0 satisfying an additional condition can be realized as a group of symplectic automorphisms of an irreducible symplectic variety deformation equivalent to Hilbn(X) of some K3 surface.
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机译：在本说明中，我们在衍生的K3表面的等效性方面解释Gaberdiel等[7]的最近结果。我们证明，Conway Group Co_0的子组之间存在自然的双重曲线，其具有秩序的级别的至少四个和曲出的D〜B（x）的辛衍生的等效等量，该射程K3表面的D〜B（x）的阶段固定稳定条件。作为一个应用程序，我们证明了每个这样的亚组g？满足额外条件的CO_0可以实现为与一些K3表面的HILBN（X）相当的IRRAFUIFIBE伴曲面变形的一组辛自相。
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