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Vanishing of the leading term
in Harish-Chandra's local character expansion

Author: Reid C. Huntsinger
Journal: Proc. Amer. Math. Soc. 124 (1996), 2229-2234
MSC (1991): Primary 22E50
MathSciNet review: 1307530
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Abstract: Harish-Chandra's formula for the character $\Theta _\pi $ of an irreducible smooth representation $\pi $ of a reductive $p$-adic group $G$ expresses $\Theta _\pi $ near $1$ as a linear combination of the Fourier transforms of nilpotent $G$-orbits in the Lie algebra of $G$. In this note, we prove that if $\pi $ is tempered but not in the discrete series, then the coefficient attached to the zero nilpotent orbit vanishes.

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Additional Information

Reid C. Huntsinger

Keywords: Character, nilpotent orbit, reductive $p$-adic group
Received by editor(s): September 7, 1994
Received by editor(s) in revised form: November 8, 1994
Communicated by: Roe Goodman
Article copyright: © Copyright 1996 American Mathematical Society

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