Realizing semisimple Lie groups as holomorphic automorphism groups of bounded domains

2025/04/04 by G. B. Shabat, Shabat, George, Alexander Tumanov +1
Mathematics · #22F50 #32M18 #Complex Variables (math.CV) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2504.03134

openalex publication_date 2025/04/04 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28

Abstract

We consider a problem whether a given Lie group can be realized as the group of all biholomorphic automorphisms of a bounded domain in the affine complex space. In an earlier paper of 1990, we proved the result for connected linear Lie groups. In this paper we prove the result for a fairly large class of Lie groups including all connected real semisimple groups. This class contains many non-linear Lie groups.

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