Geodesic
BGG sequences on spheres
Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) no. 3, pp. 509-527.

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BGG sequences on flat homogeneous spaces are analyzed from the point of view of decomposition of appropriate representation spaces on irreducible parts with respect to a maximal compact subgroup, the so called $K$-types. In particular, the kernels and images of all standard invariant differential operators (including the higher spin analogs of the basic twistor operator), i.e. operators appearing in BGG sequences, are described.
Classification : 22E30, 22E46, 35P15, 43A85
Keywords: BGG sequences; invariant differential operators; branching rules; $K$-types; complexes; homogeneous spaces 
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     title = {BGG sequences on spheres},
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Somberg, Petr. BGG sequences on spheres. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) no. 3, pp. 509-527. http://geodesic.mathdoc.fr/item/CMUC_2000__41_3_a8/