2022/10/28 by Laura Geatti, Geatti, Laura, Andrea Iannuzzi +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2210.16213
openalex publication_date 2022/10/28 · openalex created_date 2022/11/05 · openalex updated_date 2026/07/28
Let G/K be a non-compact irreducible Hermitian symmetric space of rank r and let NAK be an Iwasawa decomposition of G. By the polydisc theorem, AK/K can be regarded as the base of an r-dimensional tube domain holomorphically embedded in G/K. As every N-orbit in G/K intersects AK/K in a single point, there is a one-to-one correspondence between N-invariant domains in G/K and tube domains in the product of r copies of the upper half-plane in \C. In this setting we prove a generalization of Bochner's tube theorem. Namely, an N-invariant domain D in G/K is Stein if and only if the base Ω of the associated tube domain is convex and ``cone invariant". We also obtain a precise description of the envelope of holomorphy of an arbitrary holomorphically separable N-invariant domain over G/K.