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We have studied the symmetry properties of the bands of the layered semiconductor GaSe along the Δ direction by means of spin-resolved electron spectroscopy using circularly polarized synchrotron radiation and by means of a relativistic LAPW band-structure calculation. The photoelectron spectra show in the main a pair of weakly dispersing peaks caused by direct transitions from valence-band states with symmetries Δ59, Δ69 and Δ57, Δ68. Our data determine the spin-orbit splitting of these valence bands to be ΔEso=0.3±0.1eV. We find a gap in the unoccupied bands along Δ about 8 eV above the fundamental gap. The analysis of the photoelectron spin polarization reveals that also unoccupied states with low symmetries Δ57, Δ68 and Δ59, Δ69 are involved in excitation and emission. Spin resolved spectra measured at Auger electrons following the decay of Ga 3d core holes confirm that p derived unoccupied states exists below the vacuum level.