Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-05T04:20:02.989Z Has data issue: false hasContentIssue false

GERMS OF CHARACTERS OF ADMISSIBLE REPRESENTATIONS OF p-ADIC GENERAL LINEAR GROUPS

Published online by Cambridge University Press:  21 July 2003

Fiona Murnaghan
Affiliation:
Department of Mathematics, University of Toronto, Toronto M5S 3G3, Canada ([email protected])

Abstract

Let $G=GL_n(F)$, where $F$ is a $p$-adic field of characteristic zero and residual characteristic $p$. Assuming that $p>2n$, we compare germs of characters of irreducible admissible representations of $G$ with germs of characters of unipotent representations of direct products of general linear groups over finite extensions of $F$. We show that the character of an irreducible admissible representation has an $s$-asymptotic germ expansion, for some semisimple $s$ in the Lie algebra of $G$. Furthermore, this expansion matches with the $0$-asymptotic expansion (that is, the local character expansion) of the character of a unipotent representation of the centralizer of $s$ in $G$.

AMS 2000 Mathematics subject classification: Primary 22E50; 22E35

Type
Research Article
Copyright
2003 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)