Invariant Differential Operators for the Real Exceptional Lie Algebra $F"_4$

TL;DR

This paper systematically constructs and classifies invariant differential operators for the non-compact exceptional Lie algebra F4, focusing on reducible Verma modules and their compatibility with invariant operator induction.

Contribution

It provides a detailed classification of invariant differential operators for F4, advancing the understanding of their structure and representation theory.

Findings

Classification of reducible Verma modules over F4

Complete classification of invariant differential operators for F4

Identification of modules compatible with invariant operator induction

Abstract

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact exceptional Lie algebra $F"_4$ which is the split rank one form of the exceptional Lie algebra $F_4$. We classify the reducible Verma modules over $F_4$ which are compatible with this induction. Thus, we obtain the classification of the corresponding invariant differential operators.