Differential equations and Lie group representations

doi:10.1007/s11464-022-1008-z

Front. Math. China

2022, Vol. 17

Issue (2) : 171-225 https://doi.org/10.1007/s11464-022-1008-z

SURVEY ARTICLE

Differential equations and Lie group representations

King Fai LAI(

)

School of Mathematics and Statistics, Henan University, Kaifeng 475004, China

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Abstract

We discuss the role of differential equations in Lie group representation 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.

Keywords Differential equations Lie groups representation theory arithmetic D-modules flag variety

Corresponding Author(s): King Fai LAI

Issue Date: 23 May 2022

Cite this article:

King Fai LAI. Differential equations and Lie group representations[J]. Front. Math. China, 2022, 17(2): 171-225.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-022-1008-z
https://academic.hep.com.cn/fmc/EN/Y2022/V17/I2/171

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