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Characters and growth of admissible representations of reductive p-adic groups

Part of: Linear algebraic groups and related topics

Published online by Cambridge University Press:  13 June 2011

Ralf Meyer  and
Maarten Solleveld
Ralf Meyer
Affiliation:
Mathematisches Institut and Courant Centre ‘Higher Order Structures’, Georg-August Universität Göttingen, Bunsenstraβe 3–5, 37073 Göttingen, Germany (rameyer@uni-math.gwdg.de; maarten@uni-math.gwdg.de)
Maarten Solleveld
Affiliation:
Mathematisches Institut and Courant Centre ‘Higher Order Structures’, Georg-August Universität Göttingen, Bunsenstraβe 3–5, 37073 Göttingen, Germany (rameyer@uni-math.gwdg.de; maarten@uni-math.gwdg.de)
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Abstract

We use coefficient systems on the affine Bruhat–Tits building to study admissible representations of reductive p-adic groups in characteristic not equal to p. We show that the character function is locally constant and provide explicit neighbourhoods of constancy. We estimate the growth of the subspaces of invariants for compact open subgroups.

Keywords

reductive p-adic groupsadmissible representationsBruhat–Tits buildings

MSC classification

Secondary: 20G25: Linear algebraic groups over local fields and their integers
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 11 , Issue 2 , April 2012 , pp. 289 - 331
Copyright
Copyright © Cambridge University Press 2012

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