Representations of p-acid reductive groups and their co-compact distinguished subgroups [French]

摘要

Let G, H be reductive p-adic groups and p : H --> G a central isogeny. A. Silberger has proved that any admissible irreducible complex representation of G restricts via p to a direct sum of finitely many admissible irreducible representations of H. We prove that conversely any admissible irreducible complex representation of H occurs as a direct summand of such a restriction and extends to an admissible representation of a finite index open subgroup of G. We extend those results by linking them with algebraic properties of the categories of smooth representations of G and H. (C) 2001 Academic Press. [References: 11]