Systems of Differential Operators and Generalized Verma Modules

TL;DR

This paper completes the classification of conformally invariant second-order differential operator systems, identifying special values and homomorphism properties between generalized Verma modules in degenerate principal series.

Contribution

It provides a complete analysis of previously unresolved cases, determining the special values and standardness of homomorphisms in conformally invariant systems.

Findings

Identified special values of differential operator systems

Determined standardness of homomorphisms between Verma modules

Closed open cases from prior research

Abstract

In this paper we close the cases that were left open in our earlier works on the study of conformally invariant systems of second-order differential operators for degenerate principal series. More precisely, for these cases, we find the special values of the systems of differential operators, and determine the standardness of the homomorphisms between the generalized Verma modules, that come from the conformally invariant systems.