The isotropy groups of bounded homogeneous domains are nontrivial
The author answers the following question: Does there exist a bounded homogeneous domain \(M\) such that \(\Aut(M)\) acts freely on \(M\)? The answer is no. The proof is a simple consequence of the following well known results (1) bounded homogeneous domains are Siegel domains of second type over regular homogeneous cones; (Pijateckii-Shapiro, Gindikin and Vinberg) (2) inductive description of homogeneous regular cones by Rothaus.
scientific article; zbMATH DE number 1310844