
Journal of Lie Theory 28 (2018), No. 4, 11491164 Copyright Heldermann Verlag 2018 Singular BGG Complexes Over Isotropic 2Grassmannian Denis Husadzic Faculty of Science, University of Zagreb, Bijenicka cesta 30, 10 000 Zagreb, Croatia dhusadzi@math.hr Rafael Mrden Faculty of Civil Engineering, University of Zagreb, Fra Andrije KacicaMiosica 26, 10 000 Zagreb, Croatia rafaelm@grad.hr [Abstractpdf] \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 $\GL(2,\mbbC) \times \Sp(2n4,\mbbC)$. The constructed sequences are analogues of the BernsteinGelfandGelfand resolutions. We do this by considering the Penrose transform over an appropriate double fibration. The result differs from the Hermitian situation. Keywords: BernsteinGelfandGelfand (BGG) complexes, singular infinitesimal character, isotropic 2Grassmannian, invariant differential operators, Penrose transform. MSC: 58J10; 53C28, 53A55 [ Fulltextpdf (183 KB)] for subscribers only. 