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

Huntsinger, Reid

doi:10.1090/S0002-9939-96-03183-8

Vanishing of the leading term in Harish-Chandra’s local character expansion
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by Reid C. Huntsinger PDF

Proc. Amer. Math. Soc. 124 (1996), 2229-2234 Request permission

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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