Propagators of N anyons on a ℂ plane

Formulae for propagators of the system of N anyons on a plane ℂ, obeying the exoticstatistics v are explicitly derived in terms of v-equivariant anyonic harmonic functions, bihomogeneous with respect to both holomorphic and antiholomorphic positional variables, for the case of free particles and particles in the potential field of a harmonic oscillator. In the latter case, we consider the cases of absence and presence of a homogeneous magnetic field.