Singular BGG complexes over isotropic 2Grassmannian
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 $\operatorname{GL}(2,\mathbb{C}) \times \operatorname{Sp}(2n4,\mathbb{C})$. 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.
 Publication:

arXiv eprints
 Pub Date:
 March 2018
 arXiv:
 arXiv:1803.10497
 Bibcode:
 2018arXiv180310497H
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Representation Theory;
 Primary: 58J10;
 Secondary: 53C28;
 53A55
 EPrint:
 Corrected typos. 15 pages. Comments are welcome