Linear representations of the automorphism group of a free group

Fritz Grunewald; Alexander Lubotzky

doi:10.1007/s00039-009-0702-2

Linear representations of the automorphism group of a free group

Fritz Grunewald
, Alexander Lubotzky

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

48 Scopus citations

Abstract

Let F_n be the free group on n ≥ 2 elements and Aut(F_n) its group of automorphisms. In this paper we present a rich collection of linear representations of Aut(F_n) arising through the action of finite-index subgroups of it on relation modules of finite quotient groups of F_n. We show (under certain conditions) that the images of our representations are arithmetic groups.

Original language	English
Pages (from-to)	1564-1608
Number of pages	45
Journal	Geometric and Functional Analysis
Volume	18
Issue number	5
DOIs	https://doi.org/10.1007/s00039-009-0702-2
State	Published - Feb 2009

Keywords

Automorphism groups of free groups
Linear representations
Relation modules

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10.1007/s00039-009-0702-2

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AB - Let Fn be the free group on n ≥ 2 elements and Aut(Fn) its group of automorphisms. In this paper we present a rich collection of linear representations of Aut(Fn) arising through the action of finite-index subgroups of it on relation modules of finite quotient groups of Fn. We show (under certain conditions) that the images of our representations are arithmetic groups.

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KW - Linear representations

KW - Relation modules

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Linear representations of the automorphism group of a free group

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