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2017 A remark on Jacquet-Langlands correspondence and invariant $s$
Kazutoshi Kariyama
Tohoku Math. J. (2) 69(1): 25-33 (2017). DOI: 10.2748/tmj/1493172125


Let $F$ be a non-Archimedean local field, and let $G$ be an inner form of $\mathrm{GL}_N(F)$ with $N \ge 1$. Let $\boldsymbol{\mathrm{JL}}$ be the Jacquet--Langlands correspondence between $\mathrm{GL}_N(F)$ and $G$. In this paper, we compute the invariant $s$ associated with the essentially square-integrable representation $\boldsymbol{\mathrm{JL}}^{-1}(\rho)$ for a cuspidal representation $\rho$ of $G$ by using the recent results of Bushnell and Henniart, and we restate the second part of a theorem given by Deligne, Kazhdan, and Vignéras in terms of the invariant $s$. Moreover, by using the parametric degree, we present a proof of the first part of the theorem.


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Kazutoshi Kariyama. "A remark on Jacquet-Langlands correspondence and invariant $s$." Tohoku Math. J. (2) 69 (1) 25 - 33, 2017.


Published: 2017
First available in Project Euclid: 26 April 2017

zbMATH: 1365.22004
MathSciNet: MR3640011
Digital Object Identifier: 10.2748/tmj/1493172125

Primary: 22E50

Keywords: central simple algebra , essentially square-integrable representation , Jacquet--Langlands correspondence , Non-Archimedean local field , parametric degree , simple type

Rights: Copyright © 2017 Tohoku University


Vol.69 • No. 1 • 2017
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