Geodesic
Singular BGG Complexes Over Isotropic 2-Grassmannian
Journal of Lie theory, Tome 28 (2018) no. 4, pp. 1149-1164
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\newcommand{\Sp}{\operatorname{Sp}} \newcommand{\mbbC}{\mathbb{C}} \newcommand{\GL}{\operatorname{GL}} We construct exact sequences of invariant differential operators acting on sections of certain homogeneous vector bundles in singular infinitesimal character, over the isotropic $2$-Grassmannian. This space is equal to $G/P$, where $G$ is $\Sp(2n,\mbbC)$, and $P$ its standard parabolic subgroup having the Levi factor $\GL(2,\mbbC) \times \Sp(2n-4,\mbbC)$. The constructed sequences are analogues of the Bernstein-Gelfand-Gelfand resolutions. We do this by considering the Penrose transform over an appropriate double fibration. The result differs from the Hermitian situation.
Classification : 58J10, 53C28, 53A55
Mots-clés : Bernstein-Gelfand-Gelfand (BGG) complexes, singular infinitesimal character, isotropic 2-Grassmannian, invariant differential operators, Penrose transform 
@article{JLT_2018_28_4_JLT_2018_28_4_a11,
     author = {D. Husadzic and R. Mrden},
     title = {Singular {BGG} {Complexes} {Over} {Isotropic} {2-Grassmannian}},
     journal = {Journal of Lie theory},
     pages = {1149--1164},
     year = {2018},
     volume = {28},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JLT_2018_28_4_JLT_2018_28_4_a11/}
}
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D. Husadzic; R. Mrden. Singular BGG Complexes Over Isotropic 2-Grassmannian. Journal of Lie theory, Tome 28 (2018) no. 4, pp. 1149-1164. http://geodesic.mathdoc.fr/item/JLT_2018_28_4_JLT_2018_28_4_a11/