  The anyonic excitations of a spin-liquid can feature fractional quantum
numbers under space-group symmetries. Detecting these fractional quantum
numbers, which are analogs of the fractional charge of Laughlin quasiparticles,
may prove easier than the direct observation of anyonic braiding and
statistics. Motivated by the recent numerical discovery of spin-liquid phases
in the kagome Heisenberg antiferromagnet, we theoretically predict the pattern
of space group symmetry fractionalization in the kagome lattice chiral spin
liquid. We provide a method to detect these fractional quantum numbers in
finite-size numerics which is simple to implement in DMRG. Applying these
developments to the chiral spin liquid phase of a kagome Heisenberg model, we
find perfect agreement between our theoretical prediction and numerical
observations.
