engleski

Singular BGG complexes over isotropic 2-Grassmannian

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)xSp(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.

Bernstein-Gelfand-Gelfand (BGG) complexes ; singular infinitesimal character ; isotropic 2-Grassmannian ; invariant differential operators ; Penrose transform

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