  We study the emission of the short/hard GRB 090510 at energies > 0.1 GeV as
observed by the Large Area Telescope (LAT) onboard the Fermi satellite. The GeV
flux rises in time as t^2 and decays as t^-1.5 up to 200 s. The peak of the
high energy flux is delayed by 0.2 s with respect to the main ~MeV pulse
detected by the Fermi Gamma Burst Monitor (GBM). Its energy spectrum is
consistent with F(E)=E^-1. The time behavior and the spectrum of the high
energy LAT flux are strong evidences of an afterglow origin. We then interpret
it as synchrotron radiation produced by the forward shock of a fireball having
a bulk Lorentz factor Gamma ~ 2000. The afterglow peak time is independent of
energy in the 0.1-30 GeV range and coincides with the arrival time of the
highest energy photon (~ 30 GeV). Since the flux detected by the GBM and the
LAT have different origins, the delay between these two components is not
entirely due to possible violation of the Lorentz invariance. It is the LAT
component by itself that allows to set a stringent lower limit on the
quantum-gravity mass of 4.7 times the Planck mass.
