微分方程和李群表示

Differential Equations and Lie Group Representations

本文介绍微分方程和李群表示的关系,特别是p进理论的近期进展.我们以柏原正树的五角图形为实表示理论的参考架,然后用Berthelot的算术D模理论和Schneider-Stuhler的楼的层理论介绍关于此图的P进类比所引起由Emerton,Kisin,Patel,Huyghe,Schmidt,Strauch所做的一些工作.

We discuss the relation between differential equations and Lie group representations, in particular the recent progress in p-adic theory. We use Kashiwara’s pentagon as a reference frame for the real representation theory and then report on some work arising from its p-adic analogue by Emerton, Kisin, Patel, Huyghe, Schmidt, Strauch using Berthelot’s theory of arithmetic D-modules and Schneider-Stuhler theory of sheaves on buildings.