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The complete set of ground state wave functions for N anyons in an externalmagnetic field on the torus is found. The cases when the filling factor is lessthan or equal to one are considered. The single valued description of anyons isemployed through out by coupling bosons to a Chern-Simons field. At the end,the Chern-Simons interaction is removed by a singular gauge transformation as aresult of which the wave functions become multi-component in agreement withother studies.Comment: 10 pages, Latex document, USITP-93-0

EXACT GROUND STATE WAVE FUNCTIONS FOR N ANYONS IN A MAGNETIC FIELD ON A TORUS