Representations of some lattices into the group of analytic diffeomorphisms of the sphere S^2

In [11] it is proved that any morphism from a subgroup of finite index of SL(n,Z) to the group of analytic diffeomorphisms of S2 has a finite image as soon as n ≥ 5. The case n = 4 is also claimed to follow along the same arguments; in fact this is not straightforward and that case indeed needs a modification of the argument. In this paper we recall the strategy for n ≥ 5 and then focus on the case n = 4.