On automorphism groups of generalized Hua domains

Abstract

Hua domains, generalized Hua domains and Hua constructions, named after the great Chinese mathematician Luogeng Hua (Loo-Keng Hua), are generalizations of Cartan–Hartogs domains introduced by Weiping Yin around the end of the 20th century. In this paper, we give a complete description of automorphism groups of generalized Hua domains. We also discuss the corresponding problem for Hua constructions.

Rigidity of proper holomorphic mappings between equidimensional Hua domains

“…Then, in this case, there exists only the identity σ = 1 ∈ S 2 such that n σ(i) = n i , p σ(i) = p i for 1 ≤ i ≤ 2, and obviously Γ(H B 2 ((2, 2); (1, 2))) Aut(H B 2 ((2, 2); (1, 2))) (cf. Theorem 1.1 in Rong [23]). This means that Corollary 1.2 does not hold for the Hua domain H Ω (n; p) which is not in the standard form.…”

“…Following the reasoning in Ahn-Byun-Park [1], Rong [23] claimed a description of automorphism groups of Hua domains H Ω (n, p) in 2014. But, Lemma 3.2 in Rong [23], which is central to the proof of its main results in [23], is definitely wrong (cf. Proposition 2.4 in our paper for references).…”

“…In 2012, Ahn-Byun-Park [1] determined the automorphism group of the Cartan-Hartogs domain H Ω (n 1 ; p 1 ) by case-by-case checking only for four types of classical domains Ω. Following the reasoning in Ahn-Byun-Park [1], Rong [23] claimed a description of automorphism groups of Hua domains H Ω (n, p) in 2014. But, Lemma 3.2 in Rong [23], which is central to the proof of its main results in [23], is definitely wrong (cf.…”

The holomorphic automorphism groups of twisted Fock-Bargmann-Hartogs domains

“…If Ω is an irreducible bounded symmetric domain F and Φ is the generic norm of F , then this domain is called the Hua domain. For works related to the Hua domain, see [17], [23]. In [28], the Bergman kernel and the automorphism group of Ω m,p are studied when Ω = C n and Φ(z) = e −µ z 2 .…”

“…Although a complete description of the automorphism group of the Hua domain is already known (cf. [17], [23]), its generalization to the Hua construction, is still open. The main result of this paper gives a complete description of the automorphism group of the twisted Fock-Bargmann-Hartogs domain…”