Equivariant embeddings of Stein domains sitting inside of complex semigroups

Bernhard Krötz

Vol. 189 (1999), No. 1, 55–73

DOI: 10.2140/pjm.1999.189.55

Abstract

In this paper we prove an equivariant version of Hörmanders embedding theorem for Stein manifolds. More concretely, let G be a connected Lie group sitting in its complexification G_ℂ and D ⊆ G_ℂ a G × G-invariant Stein domain. Under slight obstructions on D we construct a Hilbert space ℋ equipped with a unitary G×G-action and a holomorphic equivariant closed embedding e D →ℋ^∗∖{0}.

Milestones

Received: 22 September 1997

Revised: 20 November 1997

Published: 1 May 1999