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arXiv · 1803.10497

Singular BGG complexes over isotropic 2-Grassmannian

Denis Husadžić·Rafael Mrđen
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Abstract

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 $\operatorname{Sp}(2n,\mathbb{C})$, and $P$ its standard parabolic subgroup having the Levi factor $\operatorname{GL}(2,\mathbb{C}) \times \operatorname{Sp}(2n-4,\mathbb{C})$. 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.

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Denis Husadžić, Rafael Mrđen. 2018-03-28. Singular BGG complexes over isotropic 2-Grassmannian. https://arxiv.org/abs/1803.10497

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