Classification of minimal representations of real simple Lie groups

TL;DR

This paper classifies minimal representations of connected simple real Lie groups (excluding type A), confirming that no new minimal representations exist beyond known ones, thus completing the classification in this area.

Contribution

It provides a complete classification of minimal representations for all connected simple real Lie groups except type A, showing no additional representations are possible.

Findings

No new minimal representations exist beyond known ones.

Complete classification of minimal representations for non-type A groups.

Confirmation that existing classifications are exhaustive.

Abstract

Based on an idea in [Gan--Savin, Represent. Theory (2005)], we give a classification of minimal representations of connected simple real Lie groups not of type $A$. Actually, we prove that there exist no new minimal representations up to infinitesimal equivalence.