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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie


IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2017: 1.49

Online
ISSN
1435-5345
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Volume 1999, Issue 508

Issues

Caractères à valeurs dans le centre de Bernstein

J.-F Dat
Published Online: 2008-06-11 | DOI: https://doi.org/10.1515/crll.1999.508.61

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 PЗ.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 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).

About the article

Received: 1998-06-23

Published Online: 2008-06-11

Published in Print: 1999-03-12


Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 1999, Issue 508, Pages 61–83, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crll.1999.508.61.

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