Special Reduced Multiplets and Minimal Representations for SO(p,q)

TL;DR

This paper classifies special reduced multiplets and minimal representations of the non-compact Lie group SO(p,q) using invariant differential operators, advancing understanding of its representation theory.

Contribution

It introduces a systematic classification of special reduced multiplets and minimal representations for SO(p,q) based on invariant differential operators.

Findings

Classification of special reduced multiplets for SO(p,q)

Identification of minimal representations within these multiplets

Development of a systematic construction method for invariant differential operators

Abstract

Using our previous results on the systematic construction of invariant differential operators for non-compact semisimple Lie groups we classify the special reduced multiplets and minimal representations in the case of SO(p,q).