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Sbornik: Mathematics, 2020, Volume 211, Issue 8, Pages 1065–1079
DOI: https://doi.org/10.1070/SM9311 (Mi sm9311) 		 
Cocompact lattices in locally pro-$p$-complete rank-2 Kac-Moody groups

I. Capdeboscqa, K. Hristovab, D. A. Rumyninac

a Mathematics Institute, University of Warwick, Coventry, UK
b School of Mathematics, University of East Anglia, Norwich, UK
c Laboratory of Algebraic Geometry and Its Applications, National Research University Higher School of Economics, Moscow
English version PDF (551 kB) Russian version article
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DOI: https://doi.org/10.1070/SM9311
Abstract: We initiate an investigation of lattices in a new class of locally compact groups: so-called locally pro-$p$-complete Kac-Moody groups. We discover that in rank 2 their cocompact lattices are particularly well-behaved: under mild assumptions, a cocompact lattice in this completion contains no elements of order $p$. This statement is still an open question for the Caprace-Rémy-Ronan completion. Using this, modulo results of Capdeboscq and Thomas, we classify edge-transitive cocompact lattices and describe a cocompact lattice of minimal covolume.
Bibliography: 22 titles.
Keywords: Kac-Moody group, lattice, building, completion.
Funding agency Grant number
HSE Basic Research Program
Ministry of Education and Science of the Russian Federation 5-100
Max Planck Institute for Mathematics
The research of D. A. Rumynin was carried out with the support of the Basic Research Program of the National Research University Higher School of Economics and the Russian Academic Excellence Project ‘5-100’ and was also supported by the Max Planck Institute for Mathematics (Bonn, Germany).
Received: 07.08.2019 and 04.05.2020
Bibliographic databases:
Document Type: Article
UDC: 512.546.3+512.817
MSC: Primary 20G44; Secondary 22E40
Language: English
Original paper language: Russian
Citation: I. Capdeboscq, K. Hristova, D. A. Rumynin, “Cocompact lattices in locally pro-$p$-complete rank-2 Kac-Moody groups”, Sb. Math., 211:8 (2020), 1065–1079
Citation in format AMSBIB
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\paper Cocompact lattices in locally pro-$p$-complete rank-2 Kac-Moody groups
\jour Sb. Math.
\yr 2020
\vol 211
\issue 8
\pages 1065--1079
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