  In this work we present solutions to Knizhnik-Zamolodchikov (KZ) equations
corresponding to conformal block wavefunctions of non-Abelian Ising- and
Fibonacci-Anyons. We solve these equations around regular singular points in
configuration space in terms of hypergeometric functions and derive explicit
monodromy representations of the braid group action. This confirms the correct
non-Abelian statistics of the solutions. One novelty of our approach is that we
explicitly keep track of spin basis states and identify conformal blocks
uniquely with such states at relevant points in moduli space.
