Heisenberg Parabolic Subgroups of Exceptional Noncompact $G_{2(2)}$ and Invariant Differential Operators

TL;DR

This paper systematically constructs invariant differential operators for the non-compact algebra G_{2(2)} using Heisenberg parabolic subalgebras, providing explicit parametrizations and new results for applications involving G_{2(2)}.

Contribution

It introduces a comprehensive method for constructing invariant differential operators on G_{2(2)} using minimal and maximal Heisenberg parabolic subalgebras, including explicit parametrizations.

Findings

Main multiplets of indecomposable elementary representations identified

Explicit parametrization of invariant differential operators provided

New results applicable to G_{2(2)} invariant analysis

Abstract

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebra $G_{2(2)}$. We use both the minimal and the maximal Heisenberg parabolic subalgebras. We give the main multiplets of indecomposable elementary representations. This includes the explicit parametrization of the invariant differential operators between the ERs. These are new results applicable in all cases when one would like to use $G_{2(2)}$ invariant differential operators.