# Singular BGG Complexes Over Isotropic 2-Grassmannian

Journal of Lie Theory 28 (2018), No. 4, 1149–1164

http://www.heldermann.de/JLT/JLT28/JLT284/jlt28054.htm

(preprint: https://arxiv.org/abs/1803.10497)

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 Sp(2n,C), and P its standard parabolic subgroup having the Levi factor GL(2,C)×Sp(2n4,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.

Keywords: Bernstein-Gelfand-Gelfand (BGG) complexes, singular infinitesimal character, isotropic 2-Grassmannian, invariant differential operators, Penrose transform.

MSC: 58J10; 53C28, 53A55.