A CONSTRUCTION OF THE SUPERCUSPIDAL REPRESENTATIONS OF GLN(F), F P-ADIC

Let F be a nondiscrete, locally compact, non-Archimedean field. In thi s paper, we construct all irreducible supercuspidal representations of G = GL(n)(F) . For each such representation pi (which we may as well assume is unitary), we give a subgroup J of G that is compact mod the center Z of G and a (finite-dimensional) representation sigma of J suc h that inducing sigma to G gives pi. The proof that all supercuspidals have been constructed appeals to a theorem (the Matching Theorem) tha t has been proved by global methods.