On the Local Langlands Conjecture for GL(n): The Cyclic Case

Let F be a locally compact nonarchimedean field, and p its residue characteristic. Let F be a separable algebraic closure of F, WF the Weil group of F over F, E a character of FX of order n, and E the corresponding character of WF. Then there exists a canonical map from the set of equivalence classes a of irreducible degree n representations of WF such that E ? a = a to the set of equivalence classes 7r of admissible irreducible supercuspidal representations of GL(n, F) verifying ( odet) ? X = 7T. This map is shown to be bijective and to preserve e-factors for pairs.