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On the action of the unitary group on the projective plane over a local field

Part of: Non-Archimedean analysis Special varieties Linear algebraic groups and related topics

Published online by Cambridge University Press:  09 April 2009

Harm Voskuil
Harm Voskuil
Affiliation:
School of Mathematics and Statistics University of SydneyNSW 2006Australia e-mail: voskuil-h@maths.su.oz.au
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Abstract

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Let G be a unitary group of rank one over a non-archimedean local field K (whose residue field has a characteristic ≠ 2). We consider the action of G on the projective plane. A G(K) equivariant map from the set of points in the projective plane that are semistable for every maximal K split torus in G to the set of convex subsets of the building of G(K) is constructed. This map gives rise to an equivariant map from the set of points that are stable for every maximal K split torus to the building. Using these maps one describes a G(K) invariant pure affinoid covering of the set of stable points. The reduction of the affinoid covering is given.

MSC classification

Secondary: 32P05: Non-Archimedean analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem) 14M17: Homogeneous spaces and generalizations 20G25: Linear algebraic groups over local fields and their integers
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 62 , Issue 3 , June 1997 , pp. 371 - 397
Copyright
Copyright © Australian Mathematical Society 1997

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