Singular BGG complexes over isotropic 2-Grassmannian

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

Corrected typos. 15 pages. Comments are welcome

Cited by in corpus (1)

• BGG complexes in singular blocks of category O