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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Low-dimensional linear representations
of $\mathrm{Aut} \: F_n,$ $n \geq 3$


Authors: A. Potapchik and A. Rapinchuk
Journal: Trans. Amer. Math. Soc. 352 (2000), 1437-1451
MSC (2000): Primary 20C15, 20F28
Published electronically: October 15, 1999
MathSciNet review: 1491874
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Abstract: We classify all complex representations of $\mathrm{Aut} \: F_n,$ the automorphism group of the free group $F_n$ $(n \geq 3),$ of dimension $\leq 2n - 2.$ Among those representations is a new representation of dimension $n + 1$ which does not vanish on the group of inner automorphisms.


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Additional Information

A. Potapchik
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
Email: apotapchik@math.uwaterloo.ca

A. Rapinchuk
Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22903
Email: asr3x@weyl.math.virginia.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02293-X
PII: S 0002-9947(99)02293-X
Received by editor(s): July 22, 1997
Received by editor(s) in revised form: September 24, 1997
Published electronically: October 15, 1999
Additional Notes: The second author was supported in part by NSF Grant DMS-9700474
Article copyright: © Copyright 1999 American Mathematical Society