Using angle-resolved inverse photoemission spectroscopy (KRIPES), we have investigated the unoccupied electronic structure of the model interface Sn/Si(111)-alpha-root3 at room temperature. In addition to a 'metallic" surface state crossing the Fermi level (E-F) near the <(K)over bar> point, we unambiguously assign a second feature of our KRIPES spectra, located around 1.5 eV above E-F to a second surface state U-2'. We will experimentally show that U-2' is an intrinsic feature of the alpha-root3 reconstruction which cannot be associated with defects. The existence of these two surface states is not compatible with the ideal T-4 model which would show either a single, half-occupied metallic band crossing E-F or an insulating phase if strong correlation effects, important for these narrow surface bands. are considered. Rather, both U-1' and U-2' receive a natural explanation, once many body effects are introduced, in the framework of a dynamical fluctuations model, where two kinds of Sn adatoms sites reminiscent of a low-temperature 3 x 3 phase do persist at room temperature. Correlated surface bands incorporating many-body effects in a non restricted way provide a complete description of the experimental surface bands and their dispersions.