Caractères à valeurs dans le centre de Bernstein
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J.-F Dat
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.χℂ 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 indGK(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).
© Walter de Gruyter
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- Caractères à valeurs dans le centre de Bernstein
- Symplectic cutting of Kähler manifolds
- Automorphism groups of 3-dimensional complex tori
- Invariants of algebraic groups
- Weights of Markov traces on Hecke algebras
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Articles in the same Issue
- On nonpositively curved euclidean submanifolds: splitting results II
- Extremal lengths of homology classes on Riemann surfaces
- Addendum and erratum to An absolute Siegel's Lemma
- Is a linear space contained in a submanifold? – On the number of derivatives needed to tell
- Caractères à valeurs dans le centre de Bernstein
- Symplectic cutting of Kähler manifolds
- Automorphism groups of 3-dimensional complex tori
- Invariants of algebraic groups
- Weights of Markov traces on Hecke algebras
- On the proportion of quadratic character twists of L-functions attached to cusp forms not vanishing at the central point
- The Pfaffian closure of an o-minimal structure
- Subvarieties of ℂn with non-extendable automorphisms
