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Differential equations and Lie group representations

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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 \({\cal D}\)-modules and Schneider-Stuhler theory of sheaves on buildings.

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Lai, K.F. Differential equations and Lie group representations. Front. Math. China 17, 171–225 (2022). https://doi.org/10.1007/s11464-022-1008-z

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