THE LOCAL LANGLANDS CORRESPONDENCE FOR GL(N) AND CONDUCTORS OF PAIRS

Let p be a prime number and F a finite extension of Q(p). Let n be a p ositive integer. To each admissible irreducible supercuspidal represen tation pi of GL(n) (F), M. Harris has attached a class sigma(pi) of se misimple continuous n-dimensional representations of the Weil group of F. We show that the map pi bar right arrow sigma(pi) induces a biject ion between equivalence classes of admissible irreducible supercuspida l representations of GL(n)(F) and equivalence classes of continuous ir reducible n-dimensional representations of the Well group of F. In add ition, we show that the correspondences sigma preserve conductors for pairs. (C) Elsevier, Paris.