Skip to main content
Journal cover image

A TWISTED YU CONSTRUCTION, HARISH-CHANDRA CHARACTERS, AND ENDOSCOPY

Publication ,  Journal Article
Fintzen, J; Kaletha, T; Spice, L
Published in: Duke Mathematical Journal
January 1, 2023

We give a modification of Yu’s construction of supercuspidal representations of a connected reductive group G over a non-Archimedean local field F . This modification restores the validity of certain key intertwining property claims made by Yu, which were recently proved to be false for the original construction. This modification is also an essential ingredient in the construction of supercuspidal L-packets in a preprint by the second author. As further applications, we prove the stability and many instances of endoscopic character identities of these supercuspidal L-packets, subject to some conditions on the base field F . In particular, for regular supercuspidal parameters, we prove all instances of standard endoscopy. In addition, we prove that these supercuspidal L-packets satisfy a recent conjecture by the second author, which, together with standard endoscopy, uniquely characterizes the local Langlands correspondence for supercuspidal L-packets (again subject to the conditions on F ). These results are based on a statement of the Harish-Chandra character formula for the supercuspidal representations arising from the twisted Yu construction.

Duke Scholars

Published In

Duke Mathematical Journal

DOI

ISSN

0012-7094

Publication Date

January 1, 2023

Volume

172

Issue

12

Start / End Page

2241 / 2301

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 0101 Pure Mathematics
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Fintzen, J., Kaletha, T., & Spice, L. (2023). A TWISTED YU CONSTRUCTION, HARISH-CHANDRA CHARACTERS, AND ENDOSCOPY. Duke Mathematical Journal, 172(12), 2241–2301. https://doi.org/10.1215/00127094-2022-0080
Fintzen, J., T. Kaletha, and L. Spice. “A TWISTED YU CONSTRUCTION, HARISH-CHANDRA CHARACTERS, AND ENDOSCOPY.” Duke Mathematical Journal 172, no. 12 (January 1, 2023): 2241–2301. https://doi.org/10.1215/00127094-2022-0080.
Fintzen J, Kaletha T, Spice L. A TWISTED YU CONSTRUCTION, HARISH-CHANDRA CHARACTERS, AND ENDOSCOPY. Duke Mathematical Journal. 2023 Jan 1;172(12):2241–301.
Fintzen, J., et al. “A TWISTED YU CONSTRUCTION, HARISH-CHANDRA CHARACTERS, AND ENDOSCOPY.” Duke Mathematical Journal, vol. 172, no. 12, Jan. 2023, pp. 2241–301. Scopus, doi:10.1215/00127094-2022-0080.
Fintzen J, Kaletha T, Spice L. A TWISTED YU CONSTRUCTION, HARISH-CHANDRA CHARACTERS, AND ENDOSCOPY. Duke Mathematical Journal. 2023 Jan 1;172(12):2241–2301.
Journal cover image

Published In

Duke Mathematical Journal

DOI

ISSN

0012-7094

Publication Date

January 1, 2023

Volume

172

Issue

12

Start / End Page

2241 / 2301

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 0101 Pure Mathematics