Invariant Differential Operators for Non-Compact Lie Groups: the $SO^*(12)$ Case

TL;DR

This paper systematically constructs invariant differential operators for the non-compact Lie algebra so*(12), providing classification results that also apply to so(6,6) via parabolic relations.

Contribution

It offers the main multiplets of indecomposable elementary representations for so*(12) and extends classification to so(6,6) using parabolic relations.

Findings

Main multiplets of indecomposable elementary representations identified.

Classification results valid for both so*(12) and so(6,6).

Advances the systematic understanding of invariant differential operators for non-compact Lie groups.

Abstract

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebra $so^*(12)$. We give the main multiplets of indecomposable elementary representations. Due to the recently established parabolic relations the multiplet classification results are valid also for the algebra $so(6,6)$ with suitably chosen maximal parabolic subalgebra.