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2000 The irreducible six-dimensional complex representations of ${\rm Aut}(F\sb 2)$ that are nontrivial on $F\sb 2$
Dragomir Ž. Đoković
Experiment. Math. 9(3): 457-465 (2000).

Abstract

Denote by $\Phi_2$ the automorphism group of the free group $F_2$ on two generators. We classify the irreducible 6-dimensional complex representations of $\Phi_2$ whose restriction to $F_2$ is nontrivial. J. Dyer, E. Formanek, and E. Grossman have shown how the Bürau representation of the braid group $B_4$ gives rise to a one-parameter family of irreducible 6-dimensional representations of $\Phi_2$. The faithfulness question for these and some other closely related representations of $\Phi_2$ is open. Our classification shows that all other 6-dimensional representations of $\Phi_2$ are not faithful.

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Dragomir Ž. Đoković. "The irreducible six-dimensional complex representations of ${\rm Aut}(F\sb 2)$ that are nontrivial on $F\sb 2$." Experiment. Math. 9 (3) 457 - 465, 2000.

Information

Published: 2000
First available in Project Euclid: 18 February 2003

MathSciNet: MR1795877

Subjects:
Primary: 20C15 , 20C40
Secondary: 20E05 , 20F36

Keywords: braid group on four strings , free group on two generators , Gröbner basis routine , irreducible finite dimensional representations

Rights: Copyright © 2000 A K Peters, Ltd.

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Vol.9 • No. 3 • 2000
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