  We performed microwave spectroscopy of an InAs nanowire between
superconducting contacts implementing a finite-length, multi-channel Josephson
weak link. Certain features in the spectra, such as the splitting by spin-orbit
interactions of the transition lines among Andreev states, have been already
understood in terms of non-interacting models. However, we identify here
additional transitions, which evidence the presence of Coulomb interactions. By
combining experimental measurements and model calculations, we reach a
qualitative understanding of these very rich Andreev spectra.
