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Proceedings of the London Mathematical Society 1999 78(2):283-333; doi:10.1112/S0024611599001689
© 1999 by London Mathematical Society
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© London Mathematical Society

Lattices of Minimal Covolume in SL2 Over Local Fields

A. Lubotzky and TH. Weigel

Institute of Mathematics, Hebrew University Jerusalem 91904, Israel. E-mail: alexlub{at}math.huji.ac.il
Mathematisches Institut, Universität Freiburg Eckerstrasse 1 D-79104, Freiburg, Germany

Received 29 October 1996. Revision received 4 November 1997.

Let K be a non-archimedean local field of characteristic 0 with residue class field not of characteristic 2. In this note we will determine the minimal covolume µSL2K/{Gamma} of a lattice {Gamma} in SL2K. Furthermore, we describe all lattices of minimal covolume in terms of their associated graphs of groups and hence up to isomorphism. 1991 Mathematics Subject Classification: 20E08, 20G25.


Present address: School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London EC1 4NS. E-mail: t.weigel{at}qmw.ac.uk


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