论文标题
轨道积分和Shalika细菌的计算
Computations of orbital integrals and Shalika germs
论文作者
论文摘要
对于一个非架构的本地领域，还要使用简化的组$ g $，我们使用与Goresky-Kottiwitz-Macpherson的方法相近（残留）特征来计算某些轨道积分的方法，但使用了不同的语言。这些轨道积分使我们能够在某些``非常椭圆形的''元素上计算出Shalika细菌的元素，该元素是GKM Hessenberg品种的某些准芬特覆盖物上的合理点的数量，这是（部分）国旗品种的亚地区。 Shalika细菌的这种值决定了所谓的非常超级代表的Harish-Chandra局部特征扩展。
For a reductive group $G$ over a non-archimedean local field, with some assumptions on (residue) characteristic we give an method to compute certain orbital integrals using a method close to that of Goresky-Kottiwitz-MacPherson but in a different language. These orbital integrals allow us to compute the Shalika germs at some ``very elliptic'' elements in terms of number of rational points on some quasi-finite covers of the Hessenberg varieties of GKM, which are subvarieties of (partial) flag varieties. Such values of Shalika germs determine the Harish-Chandra local character expansions of the so-called very supercuspidal representations.
