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Caractères à valeurs dans le centre de Bernstein

1999; De Gruyter; Volume: 1999; Issue: 508 Linguagem: Inglês

10.1515/crll.1999.508.61

1435-5345

Jean-François Dat,

Homotopy and Cohomology in Algebraic Topology

Abstract Let G be a reductive p -adic group, we are interested in finitely generated projective smooth G -modules. Let P be such a module, consider it as a З-module, where З is the Bernstein center of the category of smooth G -modules. Then we can form P ⊗ З.χ ℂ for every complex-valued character of З: it is a finite length smooth representation of G . We describe its image in the Grothendieck group of finite length smooth G -modules. To do this, we define under suitable assumptions a З-valued character on the З-admissible (but not admissible!) representation P . The case of ind G K (1) where K is a special compact open subgroup of G is an interesting example. Some of his properties are discussed and extended to other representations of K using Bushnell and Kutzko's theory of types, when G = GL( n ).