Authors: Denis Husadžić, Rafael Mrđen
Journal of Lie Theory 28 (2018), No. 4, 1149–1164
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(2n−4,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.