Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 55, Number 2 (2015), 299-320.
Endo-class and the Jacquet–Langlands correspondence
Let be a non-archimedean local field. Recently, Broussous, Sécherre, and Stevens extended the notion of an endo-class, introduced by Bushnell and Henniart for with , to an inner form of over , 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.
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
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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