Kyoto Journal of Mathematics

Endo-class and the Jacquet–Langlands correspondence

Kazutoshi Kariyama

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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

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