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Invariant distributions on projective spaces over local fields


Author: Guyan Robertson
Journal: Proc. Amer. Math. Soc. 139 (2011), 2705-2711
MSC (2010): Primary 20F65, 20G25, 51E24
DOI: https://doi.org/10.1090/S0002-9939-2011-10808-6
Published electronically: January 14, 2011
MathSciNet review: 2801609
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Abstract: Let $ \Gamma$ be an $ \widetilde A_n$ subgroup of $ \operatorname{PGL}_{n+1}(\mathbb{K})$, with $ n\ge 2$, where $ \mathbb{K}$ is a local field with residue field of order $ q$ and let $ \mathbb{P}^n_{\mathbb{K}}$ be projective $ n$-space over $ \mathbb{K}$. The module of coinvariants $ H_0(\Gamma; C(\mathbb{P}^n_{\mathbb{K}},\mathbb{Z}))$ is shown to be finite. Consequently there is no nonzero $ \Gamma$-invariant $ \mathbb{Z}$-valued distribution on $ \mathbb{P}^n_{\mathbb{K}}$.


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Additional Information

Guyan Robertson
Affiliation: School of Mathematics and Statistics, University of Newcastle, Newcastle upon Tyne, NE1 7RU, United Kingdom
Email: a.g.robertson@ncl.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-2011-10808-6
Keywords: Buildings, boundary distributions
Received by editor(s): August 3, 2010
Published electronically: January 14, 2011
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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