Osaka Journal of Mathematics

Invariance of an endo-class under the essentially tame Jacquet-Langlands correspondence

Kazutoshi Kariyama

Full-text: Open access

Abstract

Let $F$ be a non-Archimedean local field with a finite residue field. We prove that the conjecture, presented by Broussous, Sécherre, and Stevens, is verified in the essetially tame case, that is, that the Jacquet-Langlands correspondence, which was explicitly described by Bushnell and Henniart, preserves an endo-class for irreducible essentially tame representations of inner forms of $\mathrm{GL}_n(F), n \ge 1$, of parametric degree $n$. Moreover we give explicitly a parameter set for such representations of an inner form $G$ of $\mathrm{GL}_n(F)$ which contain simple characters belonging to an endo-class.

Article information

Source
Osaka J. Math., Volume 54, Number 2 (2017), 229-247.

Dates
First available in Project Euclid: 1 June 2017

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1496282422

Mathematical Reviews number (MathSciNet)
MR3657228

Zentralblatt MATH identifier
1379.22015

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

Citation

Kariyama, Kazutoshi. Invariance of an endo-class under the essentially tame Jacquet-Langlands correspondence. Osaka J. Math. 54 (2017), no. 2, 229--247. https://projecteuclid.org/euclid.ojm/1496282422


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