We consider the spectral problem resulting from the Schrodinger equati
on for a quantum system of n greater-than-or-equal-to 2 indistinguisha
ble, spinless, hard-core particles on a domain in two dimensional Eucl
idian space. For particles obeying fractional statistics, and interact
ing via a repulsive hard core potential, we provide a rigorous framewo
rk for analysing the spectral problem with its multi-valued wave funct
ions.