Invariant Plurisubharmonic Functions and Hypersurfaces on Semisimple Complex Lie Groups.
Si introducono due strutture di gruppo di Lie su un dominio di Siegel omogeneo di . Per la palla unitaria si definisce una famiglia ad un parametro di strutture intermedie; ad ognuna di esse viene associato naturalmente un nucleo riproducente ottenendo un'interpolazione tra il nucleo di Bergman ed il nucleo di Szego.
We give a Hodge-theoretic parametrization of certain real Lie group orbits in the compact dual of a Mumford-Tate domain, and characterize the orbits which contain a naive limit Hodge filtration. A series of examples are worked out for the groups , , and .
Oka theory has its roots in the classical Oka-Grauert principle whose main result is Grauert’s classification of principal holomorphic fiber bundles over Stein spaces. Modern Oka theory concerns holomorphic maps from Stein manifolds and Stein spaces to Oka manifolds. It has emerged as a subfield of complex geometry in its own right since the appearance of a seminal paper of M. Gromov in 1989.In this expository paper we discuss Oka manifolds and Oka maps. We describe equivalent characterizations...
Let be a solvable complex Lie group and a closed complex subgroup of . If the global holomorphic functions of the complex manifold locally separate points on , then is a Stein manifold. Moreover there is a subgroup of finite index in with nilpotent. In special situations (e.g. if is discrete) normalizes and is abelian.
Given a compact connected Lie group . For a relatively compact -invariant domain in a Stein -homogeneous space, we prove that the automorphism group of is compact and if is semisimple, a proper holomorphic self mapping of is biholomorphic.
Let 𝓓 be a symmetric Siegel domain of tube type and S be a solvable Lie group acting simply transitively on 𝓓. Assume that L is a real S-invariant second order operator that satisfies Hörmander's condition and annihilates holomorphic functions. Let H be the Laplace-Beltrami operator for the product of upper half planes imbedded in 𝓓. We prove that if F is an L-Poisson integral of a BMO function and HF = 0 then F is pluriharmonic. Some other related results are also considered.