  We present the next-to-leading order partonic cross sections involving an
electroweak vector boson and four massless partons (quarks, gluons or long
living gluinos) in a general gauge theory with a simple Lie Group. The vector
boson couples to a massless lepton pair and a quark-antiquark pair. The cross
sections are given in terms of group independent kinematical functions
multiplying the eigenvalues of the Casimir operators of the Lie group. This
kind of color decomposition is required for the calculation of O($\alpha_s^3$)
corrections to the group independent kinematical functions in the four-jet
production cross sections in electron-positron annihilation. The knowledge of
these corrections facilitates the simultaneous precision meaurement of the
strong coupling and the color charge factors using the four-jet LEP or SLC data
as well as the test whether these data favour or exclude the existence of a
light gluino.
