Correspondance de Jacquet–Langlands explicite II. Le cas de degréégal à la caractéristique résiduelle

Abstract:

Let F be a non-Archimedean locally compact field, and let p be its residual characteristic. Put G=GL _p (F) and let G ^′=D _×, where $D$ is a division algebra with centre F and of degree p ² over F. The Jacquet–Langlands correspondence is a bijection between the discrete series of G and that of G ^′. We describe this explicitly, in terms of Carayol's parametrization of these discrete series.