Nonstandard operators in Grassmannian geometry

TL;DR

This paper constructs curved nonstandard operators on Grassmannians using curved Casimir operators, highlighting their limitations with torsion and demonstrating they are not strongly invariant.

Contribution

It introduces a new construction of curved nonstandard operators on Grassmannians and analyzes their invariance properties.

Findings

Construction of curved nonstandard operators using curved Casimir operators.

The construction fails in the presence of torsion.

Nonstandard operators are shown not to be strongly invariant.

Abstract

We present a construction of curved analogues of the nonstandard operators on Grassmannians parallel to the construction of the Paneitz operator via the curved Casimir operator, but technically more demanding. In particular, the construction breaks down in the presence of torsion. In the second part, we prove that the nonstandard operators are not strongly invariant.