Bounded domains with prescribed group of automorphisms.
In this note we explain a way to associate to any number field some connected complex abelian Lie groups. Further, we study the case of non-totally real cubic number fields, and we see that they are intimately related with the Cousin groups (toroidal groups) of complex dimension and rank .
Let be a quasi-Hermitian Lie group with Lie algebra and be a compactly embedded subgroup of . Let be a regular element of which is fixed by . We give an explicit -equivariant diffeomorphism from a complex domain onto the coadjoint orbit of . This generalizes a result of [B. Cahen, Berezin quantization and holomorphic representations, Rend. Sem. Mat. Univ. Padova, to appear] concerning the case where is associated with a unitary irreducible representation of which is holomorphically...