Journal of Lie Theory

no. 4
Singular BGG Complexes Over Isotropic 2-Grassmannian
Denis Husadzic1; Rafael Mrden2
1Faculty of Science, University of Zagreb, Bijenicka cesta 30, 10 000 Zagreb, Croatia
2Faculty of Civil Engineering, University of Zagreb, Fra Andrije Kacica-Miosica 26, 10 000 Zagreb, Croatia
Journal of Lie Theory, Volume 28 (2018) no. 4, pp. 1149-1164
\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.
DOI: 10.5802/jolt.1043
Classification: 58J10, 53C28, 53A55
Keywords: Bernstein-Gelfand-Gelfand (BGG) complexes, singular infinitesimal character, isotropic 2-Grassmannian, invariant differential operators, Penrose transform

Denis Husadzic  1 ; Rafael Mrden  2

1 Faculty of Science, University of Zagreb, Bijenicka cesta 30, 10 000 Zagreb, Croatia
2 Faculty of Civil Engineering, University of Zagreb, Fra Andrije Kacica-Miosica 26, 10 000 Zagreb, Croatia 
Denis Husadzic; Rafael Mrden. Singular BGG Complexes Over Isotropic 2-Grassmannian. Journal of Lie Theory, Volume 28 (2018) no. 4, pp. 1149-1164. doi: 10.5802/jolt.1043
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     title = {Singular {BGG} {Complexes} {Over} {Isotropic} {2-Grassmannian}},
     journal = {Journal of Lie Theory},
     pages = {1149--1164},
     year = {2018},
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