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

Published online by Cambridge University Press:  09 April 2009

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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1997

References

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