2008/07/13 by Alan Huckleberry, Joseph A. Wolf, Huckleberry, Alan +1
Mathematics · #14F05 #22E46 #32F10 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Representation Theory (math.RT) #math.CV #math.RT #msc:14F05 #msc:22E46 #msc:32F10
paper · pdf · doi:10.48550/arxiv.0807.2062
9 pages
arxiv created 2008/07/13 · openalex publication_date 2008/07/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the study of complex flag manifolds, flag domains and their cycle spaces, a key point is the fact that the cycle space \mathcal MD of a flag domain D is a Stein manifold. That fact has a long history. The earliest approach relied on construction of a strictly plurisubharmonic function on \mathcal MD, starting with a q--convex exhaustion function on D, where q is the dimension of a particular maximal compact subvariety of D (we use the normalization that 0--convex means Stein). Construction of that exhaustion function on D required that D be measurable. In that case the exhaustion on D was transferred to \mathcal MD, using a special case of a method due to Barlet. Here we do the opposite: we use an incidence method to construct a canonical plurisubharmonic exhaustion function on \mathcal MD and use it in turn to construct a canonical q--convex exhaustion function on D. This promises to have strong consequences for cohomology vanishing theorems and the construction of admissible representations of real reductive Lie groups.