Nonarchimedean Flag Domains and Semistability
Research Report 98-35
Date: 23 December 1998
Let G be a simply connected absolutely almost simple linear algebraic
group defined over a nonarchimedean local field K.
Let X be a projective homogeneous variety for G.
We consider the analytic subset Y of X that consists of the
points that are semistable for all maximal K-split tori of G with
respect to a fixed ample line bundle. The linearization of the torus
action is obtained by restricting the unique G-linearization of this
linebundle. We define a map that associates to each point of Y a
convex subset of the building. This map is defined by using semistability
over the ring of integers of K.
For split groups we give a partial description of the image of
this map. We prove that in certain cases this is actually a complete
description of the image of the map.
nonarchimedean local field. semisimple groups. affine buildings.
projective homogeneous varieties. semistability.
AMS Subject Classification (1991)
Secondary: 32P05, 14G20
The paper is available in the following forms:
- TeX dvi format:
- 1998-35.dvi.gz (84kB) or
- 1998-35.ps.gz (151kB) or
To minimize network load, please choose the smaller gzipped .gz form if
and only if your browser client supports it.
Sydney Mathematics and Statistics