Abstract

Let F be a p-adic field of characteristic 0. For odd primes ℓ with certain tameness restrictions, techniques due to Assem allow us to write supercuspidal characters of SL (F) in terms of a family of distributions defined by Kazhdan. Following an argument of Harish-Chandra, we derive an integral formula for these distributions. Results of DeBacker and Kazhdan allow us to evaluate this integral formula. This in turn gives supercuspidal character formulas for SL (F), explicit up to the constants appearing in the GL (F) local character expansion. Our result also describes the explicit local Langlands correspondence for those positive-depth supercuspidal representations of GL (F) which do not restrict irreducibly to SL (F).

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 51-100
Launched on MUSE
2005-02-02
Open Access
No
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