Parabolic nilradicals of Heisenberg type, II

TL;DR

This paper explores the structure of parabolic geometries linked to parabolic subalgebras with generalized Heisenberg nilradicals in real simple non-compact Lie algebras, focusing on their geometric properties and conformal infinities.

Contribution

It provides a detailed analysis of parabolic geometries and harmonic spaces associated with parabolic subalgebras of Heisenberg type, extending previous classifications.

Findings

Characterization of parabolic geometries with Heisenberg-type nilradicals

Description of harmonic spaces with these geometries as conformal infinities

Insights into the Riemannian geometry of the associated spaces

Abstract

Every real simple non-compact Lie algebra not isomorphic to $\mathfrak{so}(1,n)$ contains a unique standard parabolic subalgebra whose nilradical is a generalized Heisenberg algebra. Here we discuss the associated parabolic geometries and the riemannian geometry of the harmonic spaces having the former as conformal infinities.