On a characterization of unbounded homogeneous domains with boundaries of light cone type

TL;DR

This paper characterizes unbounded homogeneous domains with light cone boundary types by analyzing their automorphism groups, providing a group-theoretic description, proving non-existence of compact quotients, and presenting a counterexample.

Contribution

It offers a detailed group-theoretic characterization of these domains and clarifies their quotient structure, including a counterexample to previous assumptions.

Findings

Automorphism groups of these domains are explicitly determined.

Non-existence of compact quotients of such domains is established.

A counterexample to the existing characterization is provided.

Abstract

We determine the automorphism groups of unbounded homogeneous domains with boundaries of light cone type. Furthermore we present the group-theoretic characterization of the domain. As a corollary we prove the non-existence of compact quotients of a unbounded homogeneous domain. We also give a counterexample of the characterization.