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

Published online by Cambridge University Press:  21 July 2003

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

Keywords

characteradmissible representationFourier transformorbital integralHecke algebra
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 2 , Issue 3 , July 2003 , pp. 409 - 481
Copyright
2003 Cambridge University Press

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