The dynamics of Aut(F_n) on redundant representations

Details The dynamics of Aut(F_n) on redundant representations The dynamics of Aut(F_n) on redundant representations

2011-04-25

arxiv.org/abs/1104.4774v1

Mathematics

Dynamical Systems

18 pages

Scientific paper

We study some dynamical properties of the canonical Aut(F_n)-action on the space R_n(G) of redundant representations of the free group F_n in G, where G is the group of rational points of a simple algebraic group over a local field. We show that this action is always minimal and ergodic, confirming a conjecture of A. Lubotzky. On the other hand for the classical cases where G=SL(2,R) or SL(2,C) we show that the action is not weak mixing, in the sense that the diagonal action on R_n(G)^2 is not ergodic.

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