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The local character expansion near a tame, semisimple element
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 129, Number 2, April 2007
- pp. 381-403
- 10.1353/ajm.2007.0005
- Article
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Consider the character of an irreducible admissible representation of a p-adic reductive group. The Harish-Chandra-Howe local expansion expresses this character near a semisimple element as a linear combination of Fourier transforms of nilpotent orbital integrals. Under mild hypotheses, we describe an explicit region on which the local character expansion is valid. We assume neither that the group is connected, nor that the underlying field has characteristic zero.