A systematic exposition is given of the theory of invariant differential operators on a not necessarily reductive homogeneous space. This exposition is modelled on Helgason's treatment of the general reductive case and the special non-reductive case of the space of horocycles. As a final application the differential operators on (not a priori reductive) isotropic pseudo-Riemannian spaces are characterized.
Algebraically Independent Generators for the Algebra of Invariant Differential Operators on $\mathrm{SL}_n(\mathbb R)/\mathrm{SO}_n(\mathbb R)$
Langlands Duality and Invariant Differential Operators
Erratum and Addendum to: Invariant Differential Operators and Eigenspace Representations on an Affine Symmetric Space
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