Quantum statistics of ideal parafermi gases: The Slater quasi-determinant

The wave function ψ (1,2,3,...,N) of a gas of identical two-dimensional exotic particles of spin 1/M (mod 1), M = 2,3,... is constructed. It is shown that ψ (1,2,3,...,N) obeys a generalized Pauli exclusion principle according to which no more than (M - 1) identical particles of spin 1/M (mod 1) can live in the same quantum state. The Fermi nilpotency and the Bose condensation are recovered as special cases. Examples are given.