Correspondance de Howe: paires duales de type II

Details Correspondance de Howe: paires duales de type II Correspondance de Howe: paires duales de type II

2007-09-27

arxiv.org/abs/0709.4384v1

Mathematics

Representation Theory

Scientific paper

In this article, we give a new method for proving Howe correspondence in the case of dual pairs of type $({\rm GL}_n, {\rm GL}_m)$ 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.

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