Kyoto Journal of Mathematics

Endo-class and the Jacquet–Langlands correspondence

Kazutoshi Kariyama

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Abstract

Let F be a non-archimedean local field. Recently, Broussous, Sécherre, and Stevens extended the notion of an endo-class, introduced by Bushnell and Henniart for GL N ( F ) with N 1 , to an inner form of GL N ( F ) over F , and conjectured that this endo-class for discrete series representations is preserved by the Jacquet–Langlands correspondence. Explicit realizations of the correspondence are given by Silberger and Zink for level-zero discrete series representations and by Bushnell and Henniart for totally ramified ones. In this paper, we show that these realizations confirm the conjecture.

Article information

Source
Kyoto J. Math., Volume 55, Number 2 (2015), 299-320.

Dates
Received: 29 November 2013
Accepted: 5 March 2014
First available in Project Euclid: 11 June 2015

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1433982757

Digital Object Identifier
doi:10.1215/21562261-2871767

Mathematical Reviews number (MathSciNet)
MR3356075

Zentralblatt MATH identifier
1361.22007

Subjects
Primary: 22E50: Representations of Lie and linear algebraic groups over local fields [See also 20G05]

Keywords
non-archimedean local field central simple algebra the Jacquet–Langlands correspondence essentially square-integrable representation ps-character endo-class

Citation

Kariyama, Kazutoshi. Endo-class and the Jacquet–Langlands correspondence. Kyoto J. Math. 55 (2015), no. 2, 299--320. doi:10.1215/21562261-2871767. https://projecteuclid.org/euclid.kjm/1433982757


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References

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