Suppose we have a galaxy at redshift z=4 with monochromatic UV luminosity λUV *LUV = 4.2×1046 erg /s and an absolute K -band magnitude of K = −23.5 mag (in the AB system). Assuming a K -band absolute magnitude M⊙,AB = 5.14 for the sun, how can i determine the luminosity L_K of the galaxy ?? I am a little confused with the AB magnitude system. Should i also take into account K-correction ?