Correspondance de Howe: paires duales de type II

In this article, we give a new method for proving Howe correspondence in the case of dual pairs of type $({\mathrm{G}\mathrm{L}}_n,{\mathrm{G}\mathrm{L}}_m)$ over a non-Archimedean locally compact field $F$. The proof consists in combining a study on Kudla’s filtration with the results of a previous article of the autor about the irreducibility of a parabolically induced representation. The proof is valid for $F$ of any characteristic and allows us to make the correspondence explicit in terms of Langlands parameters.