  Non-trivial braid-group representations appear as non-Abelian quantum
statistics of emergent Majorana zero modes in one and two-dimensional
topological superconductors. Here, we generate such representations with
topologically protected domain-wall modes in a classical analogue of the Kitaev
superconducting chain, with a particle-hole like symmetry and a Z2 topological
invariant. The mid-gap modes are found to exhibit distinct fusion channels and
rich non-Abelian braiding properties, which are investigated using a T-junction
setup. We employ the adiabatic theorem to explicitly calculate the braiding
matrices for one and two pairs of these mid-gap topological defects.
