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 ℓ ( 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 ℓ ( F ), explicit up to the constants appearing in the GL ℓ ( F ) local character expansion. Our result also describes the explicit local Langlands correspondence for those positive-depth supercuspidal representations of GL ℓ ( F ) which do not restrict irreducibly to SL ℓ ( F ).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.