$\mathcal{D}$-modules and characters of semisimple Lie groups

Abstract

A famous theorem of Harish-Chandra asserts that all invariant eigendistributions on a semisimple Lie group are locally integrable functions. We show that this result and its extension to symmetric pairs are consequences of an algebraic property of the holonomic $\mathcal{D}$-module defined by Hotta and Kashiwara.