粘合抛物特征层
Gluing parabolic character sheaves
AI总结：
该研究引入并研究伴随型约化群对应Vinberg半群非退化轨迹上幂幺特征层范畴，证明其偏对象可由抛物特征层粘合，应用中证明He的猜想并否定Lusztig关于Steinberg特征层中间扩张的猜想。
AI中文摘要：
我们引入并研究伴随型约化群对应的Vinberg半群非退化轨迹上的幂幺特征层范畴，证明该范畴中合适的偏对象可由各层上的偏抛物特征层粘合而成。作为应用，我们研究从该群到其奇妙紧化的简单幂幺特征层的中间扩张，证明了He的一个猜想，同时否定了Lusztig关于Steinberg特征层中间扩张的一个猜想。
英文摘要：
We introduce and study the category of unipotent character sheaves on the non-degenerate locus of the Vinberg semigroup associated to a reductive group of adjoint type. We show that appropriate perverse objects in this category can be glued from perverse parabolic character sheaves on the strata. As an application, we study the intermediate extensions of simple unipotent character sheaves from the group to its wonderful compactification, proving a conjecture of He. We also disprove a conjecture of Lusztig regarding the intermediate extension of the Steinberg character sheaf.
