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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
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
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- Research Article
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- 2003 Cambridge University Press
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