Strongly invariant differential operators on parabolic geometries modelled on $Gr(3,3)$

Abstract

We consider the curved geometries modelled on the homogeneous space $G/P$, where $G=SL(6,\mathbb{R})$ acts transitively on the Grassmannian $Gr(3,3)$ of three-dimensional subspaces in ${\mathbb{R}}^6$, and $P$ is the corresponding isotropic subgroup. We classify the strongly invariant operators between sections of vector bundles induced on such geometries by irreducible $P$-modules, i.e., those obtained via homomorphisms of semi-holonomic Verma modules.

17 pages