The dynamics of Aut(Fn) on redundant representations
Abstract
We study some dynamical properties of the canonical Aut(Fn)-action on the space Rn(G) of redundant representations of the free group Fn 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 Rn(G)2 is not ergodic.
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