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Commensurators of some non-uniform tree lattices and Moufang twin trees

Peter Abramenko·Bertrand Remy
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Abstract

Sh. Mozes showed that the commensurator of the lattice ${\rm PSL}_2 \bigl({\bf F}_p[t{}^{-1}] \bigr)$ is dense in the full automorphism group of the Bruhat-Tits tree of valency $p+1$, the latter group being much bigger than ${\rm PSL}_2 \bigl({\bf F}_p((t)) \bigr)$. By G.A. Margulis' criterion, this density is a generalized arithmeticity result. We show that the density of the commensurator holds for many tree-lattices among those called of Nagao type by H. Bass and A. Lubotzky. The result covers many lattices obtained via Moufang twin trees.

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Peter Abramenko, Bertrand Remy. 2004-02-18. Commensurators of some non-uniform tree lattices and Moufang twin trees. https://arxiv.org/abs/math/0402299

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