论文标题
通用施普申函对应的一种新方法
A new approach to the generalized Springer correspondence
论文作者
论文摘要
Nilpotent锥体的弹簧分辨率用于给出Weyl基团的几何形状结构。 Borho和MacPherson通过将分解定理应用于Springer分辨率，从而获得Springer对应关系，从而建立了一个从不可减至的Weyl组表示形式到Nilpotent锥上简单的Eporivariant brove sheaves。在本手稿中，我们使用第一作者定义的品种考虑了弹簧分辨率的概括。我们的主要结果表明，在A型情况下，将分解定理应用于该地图，如Lusztig的广义Springer对应关系所预测的那样，具有多重性上的尼尔粘锥上的所有简单变形带。
The Springer resolution of the nilpotent cone is used to give a geometric construction of the irreducible representations of Weyl groups. Borho and MacPherson obtain the Springer correspondence by applying the decomposition theorem to the Springer resolution, establishing an injective map from the set of irreducible Weyl group representations to simple equivariant perverse sheaves on the nilpotent cone. In this manuscript, we consider a generalization of the Springer resolution using a variety defined by the first author. Our main result shows that in the type A case, applying the decomposition theorem to this map yields all simple perverse sheaves on the nilpotent cone with multiplicity as predicted by Lusztig's generalized Springer correspondence.
