Remote Access Journal of the American Mathematical Society
Green Open Access

Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)

 
 

 

Regular supercuspidal representations


Author: Tasho Kaletha
Journal: J. Amer. Math. Soc. 32 (2019), 1071-1170
MSC (2010): Primary 22E50, 11S37, 11F70
DOI: https://doi.org/10.1090/jams/925
Published electronically: July 18, 2019
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that, in good residual characteristic, most supercuspidal representations of a tamely ramified reductive $ p$-adic group $ G$ arise from pairs $ (S,\theta )$, where $ S$ is a tame elliptic maximal torus of $ G$, and $ \theta $ is a character of $ S$ satisfying a simple root-theoretic property. We then give a new expression for the roots of unity that appear in the Adler-DeBacker-Spice character formula for these supercuspidal representations and use it to show that this formula bears a striking resemblance to the character formula for discrete series representations of real reductive groups. Led by this, we explicitly construct the local Langlands correspondence for these supercuspidal representations and prove stability and endoscopic transfer in the case of toral representations. In large residual characteristic this gives a construction of the local Langlands correspondence for almost all supercuspidal representations of reductive $ p$-adic groups.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Journal of the American Mathematical Society with MSC (2010): 22E50, 11S37, 11F70

Retrieve articles in all journals with MSC (2010): 22E50, 11S37, 11F70


Additional Information

Tasho Kaletha
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109

DOI: https://doi.org/10.1090/jams/925
Received by editor(s): March 19, 2017
Received by editor(s) in revised form: October 16, 2018, January 28, 2019, and April 17, 2019
Published electronically: July 18, 2019
Additional Notes: This research was supported in part by NSF grants DMS-1161489, DMS-1801687 and a Sloan Fellowship
Article copyright: © Copyright 2019 American Mathematical Society