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

TL;DR

This paper classifies strongly invariant differential operators on curved geometries modeled on the Grassmannian of 3-planes in 6-dimensional space, using representation theory of semi-holonomic Verma modules.

Contribution

It provides a classification of invariant operators on parabolic geometries modeled on $Gr(3,3)$, extending the understanding of invariant differential operators in this setting.

Findings

Classification of strongly invariant operators achieved

Operators characterized via homomorphisms of semi-holonomic Verma modules

Results applicable to geometries modeled 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.