  We investigate the role played by large diffeomorphisms of quantum Isolated
Horizons for the statistics of LQG Black Holes by means of their relation to
the braid group. To this aim the symmetries of Chern-Simons theory are
recapitulated with particular regard to the aforementioned type of
diffeomorphisms. For the punctured spherical horizon, these are elements of the
mapping class group of $S^2$, which is almost isomorphic to a corresponding
braid group on this particular manifold. The mutual exchange of quantum
entities in two dimensions is achieved by the braid group, rendering the
statistics anyonic. With this we argue that the quantum Isolated Horizon model
of LQG based on $SU(2)_k$-Chern-Simons theory explicitly exhibits non-abelian
anyonic statistics. In this way a connection to the theory behind the
fractional quantum Hall effect and that of topological quantum computation is
established, where non-abelian anyons play a significant role.
