Cusps of lattices in rank 1 lie groups over local fields

Title: Cusps of lattices in rank 1 lie groups over local fields
Creator: Baumgartner, Udo
Relation: Geometriae Dedicata Vol. 91, Issue 1, p. 17-46
Publisher Link: http://dx.doi.org/10.1023/A:1024985017201
Publisher: Springer Netherlands
Resource Type: journal article
Date: 2003
Description: Let G be the group of rational points of a semisimple algebraic group of rank 1 over a non-Archimedean local field. We improve upon Lubotzky’s analysis of graphs of groups describing the action of lattices in G on its Bruhat–Tits tree assuming a condition on unipotents in G. The condition holds for all but a few types of rank 1 groups. A fairly straightforward simplification of Lubotzky’s definition of a cusp of a lattice is the key step to our results. We take the opportunity to reprove Lubotzky’s part in the analysis from this foundation.
Subject: graph of groups; lattice; local field; semisimple algebraic group; structure theorem
Identifier: uon:2406
Identifier: http://hdl.handle.net/1959.13/29124
Identifier: ISSN:0046-5755
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