Nonarchimedean Flag Domains and Semistability

Author

Harm Voskuil

Status

Research Report 98-35
Date: 23 December 1998

Abstract

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.

Key phrases

nonarchimedean local field. semisimple groups. affine buildings. projective homogeneous varieties. semistability.

AMS Subject Classification (1991)

Primary: 22E35
Secondary: 32P05, 14G20

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