Over the past 2 decades, there has been much progress on the classification of symplectic linear quotient singularities V/G admitting a symplectic (equivalently, crepant) resolution of singularities. The classification is almost complete but there is an infinite series of groups in dimension 4—the symplectically primitive but complex imprimitive groups—and 10 exceptional groups up to dimension 10, for which it is still open. In this paper, we treat the remaining infinite series and prove that for all but possibly 39 cases there is no symplectic resolution. We thereby reduce the classification problem to finitely many open cases. We furthermore prove non-existence of a symplectic resolution for one exceptional group, leaving \(39+9=48\) open cases in total. We do not expect any of the remaining cases to admit a symplectic resolution.

在过去的 20 年里，辛线性商奇点V / G的分类取得了很大进展，承认奇点的辛（等效，蠕变）分辨率。分类几乎是完整的，但在第 4 维存在无限系列的群——辛原始但复杂的非原始群——以及 10 维直到第 10 维的异常群，它仍然是开放的。在本文中，我们处理剩余的无穷级数并证明除了可能的 39 种情况外，所有情况都没有辛解。因此，我们将分类问题减少到有限多个开放案例。我们进一步证明了一个例外群的辛分解不存在，留下\(39+9=48\)共有未结案件。我们不希望任何剩余的案例承认辛解决。