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We establish necessary and sufficient conditions for the globalhypoellipticity of $G$-invariant operators on homogeneous vector bundles. Thesecriteria are established in terms of the corresponding matrix-valued symbols asdeveloped by Ruzhansky and Turunen and extended in [7] to homogeneousvector-bundles.

Global hypoellipticity of $G$-invariant operators on homogeneous vector bundles