ON THE GLUON PLASMON SELF-ENERGY AT O(G)

The next-to-leading order contribution delta IImu nu (omega, q) to the polarization function of the hot gluon system is analysed at nonzero wave vectors q. Using Braaten-Pisarski resummation and general covaria nt gauges, delta IImu nu is found to be gauge-fixing independent and t ransverse on the longitudinal mass-shell. The real part of the longitu dinal component delta IIl is UV and IR stable (for real q). At imagina ry q it is IR singular, and at the point omega = 0, q(2) = -3m(2) it c oincides with the result of Rebhan for next-to-leading order Debye scr eening. When q approaches the lightcone, delta IIl diverges like 1/roo t omega(2)-q(2) reflecting the breakdown of the Braaten-Pisarski decom position scheme in this limit.