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Words have bounded width in $\operatorname{SL}(n,\mathbb{Z})$

Part of: Other groups of matrices Forms and linear algebraic groups

Published online by Cambridge University Press:  13 June 2019

Nir Avni  and
Chen Meiri
Nir Avni
Affiliation:
Department of Mathematics, Northwestern University, Evanston IL, USA email [email protected]
Chen Meiri
Affiliation:
Department of Mathematics, Technion, Haifa, Israel email [email protected]
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Abstract

We prove two results about the width of words in $\operatorname{SL}_{n}(\mathbb{Z})$. The first is that, for every $n\geqslant 3$, there is a constant $C(n)$ such that the width of any word in $\operatorname{SL}_{n}(\mathbb{Z})$ is less than $C(n)$. The second result is that, for any word $w$, if $n$ is big enough, the width of $w$ in $\operatorname{SL}_{n}(\mathbb{Z})$ is at most 87.

Keywords

arithmetic groupsword width

MSC classification

Primary: 20H05: Unimodular groups, congruence subgroups 11E57: Classical groups
Type
Research Article
Information
Compositio Mathematica , Volume 155 , Issue 7 , July 2019 , pp. 1245 - 1258
Copyright
© The Authors 2019 

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