Quotients of the crown domain by a proper action of a cyclic group

TL;DR

This paper proves that quotients of the crown domain by proper cyclic group actions are Stein and that the crown domain itself is taut, extending understanding of complex structures on symmetric space quotients.

Contribution

It establishes that quotients of the crown domain by proper cyclic group actions are Stein and shows the crown domain is taut, providing new insights into complex geometry of symmetric spaces.

Findings

Quotients of the crown domain by proper cyclic group actions are Stein.

The crown domain is taut.

Analogous results hold for certain nilpotent subgroups.

Abstract

Let G/K be an irreducible Riemannian symmetric space of the non-compact type and denote by \Xi the associated crown domain. We show that for any proper action of a cyclic group \Gamma the quotient \Xi/\Gamma is Stein. An analogous statement holds true for discrete nilpotent subgroups of a maximal split-solvable subgroup of G. We also show that \Xi is taut.