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Journal of Lie Theory 28 (2018), No. 4, 1149--1164
Copyright Heldermann Verlag 2018

Singular BGG Complexes Over Isotropic 2-Grassmannian

Denis Husadzic
Faculty of Science, University of Zagreb, Bijenicka cesta 30, 10 000 Zagreb, Croatia

Rafael Mrden
Faculty of Civil Engineering, University of Zagreb, Fra Andrije Kacica-Miosica 26, 10 000 Zagreb, Croatia


\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.

Keywords: Bernstein-Gelfand-Gelfand (BGG) complexes, singular infinitesimal character, isotropic 2-Grassmannian, invariant differential operators, Penrose transform.

MSC: 58J10; 53C28, 53A55

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