CLASSIFICATION OF CONFIGURATIONS OF SYSTEMS OF IDENTICAL PARTICLES ONFINITE SETS

All possible configurations of a system of N identical particles are c lassified for the case when the configuration space Q of a single part icle reduces to a finite set. The classification is achieved by means of a combinatorial analogue of the duality of Weyl. Two groups: the Pa uli group permuting identical particles, and the symmetric group on Q, act on the Nth Cartesian power of a. These actions mutually commute, and their orbit structure is classified by appropriate epikernels. Mor eover, each stratum of each group is invariant under the dual action, which yields a coarsening of permutation representations, acting on ap propriate sets of orbits. It is shown that such a coarsening recovers the geometric symmetry for the case when particles are indistinguishab le.