The k-edge and L edge of an atom refers to the minimum energy (or maximum wavelength) photon (UV or x-ray) that can remove an (photo) electron from the K or L shells (usually meaning ionize), such that other bound electrons cascade down to fill the vacancies. The photon energies correspond to "edges" in a plot of photon attenuation vs. photon energy where there is a sudden large increase in the attenuation coecfficient. Figure 1 in this reference shows a k-shell photoelectron ejection, with the possible atomic electron cascades. http://www.bruker-axs.de/fileadmin/user_upload/xrfintro/sec1_1.html
L(2,3) may refer to the electron transition that fills the L shell vacancy (M-shell to L-shell)