N=1, D=3 SUPERANYONS, OSP(2-VERTICAL-BAR-2), AND THE DEFORMED HEISENBERG ALGEBRA

We introduce an N=1 supersymmetric generalization of the mechanical sy stem describing a particle with fractional spin in D=1+2 dimensions an d being classically equivalent to the formulation based on the Dirac m onopole two-form. The model introduced;possesses hidden invariance und er the N=2 Poincare supergroup with a central charge saturating the BP S bound. At the classical level-the model admits a Hamiltonian formula tion with two first class constraints on the phase space T(R-1,R-2)x L-1\1, where the Kahler supermanifold L(1\1)congruent to OSp(2\2)/U(1\ 1) is a minimal superextension of the Lobachevsky plane. The model is quantized by combining the geometric quantization on L-1\1 and the Dir ac quantization with respect to the first class constraints. The const ructed quantum theory describes a supersymmetric doublet of fractional spin particles. The space of quantum superparticle states with a fixe d momentum is embedded into the Pock space of a deformed bosonic oscil lator.