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June 2019 Classification of Very Cuspidal Representations of $\mathrm{GL}_m(D)$
Kazutoshi KARIYAMA
Tokyo J. Math. 42(1): 285-327 (June 2019). DOI: 10.3836/tjm/1502179296

Abstract

Let $\mathrm{F}$ be a non-Archimedean local field with finite residue field. In this paper, we generalize a classification of {\it generic} elements of the general linear group $\mathrm{GL}_n(\mathrm{F})$, $n \geqq 1$ that generate fields of degree $n$ over $\mathrm{F}$ and are {\it minimal} over $\mathrm{F}$, which was given by Hijikata, to an inner form $\mathrm{G}$ of $\mathrm{GL}_n(\mathrm{F})$, and by using the results of Dott [13], we classify supercuspidal representations of $\mathrm{G}$ that are induced from {\it very cuspidal} representations of maximal compact mod center, open subgroups, which are defined in terms of generic elements. This classification generalizes that of {\it epipelagic} supercuspidal representations of $\mathrm{G}$ which was given by Bushnell and Henniart for $\mathrm{GL}_n(\mathrm{F})$ and by Imai and Tsushima for $\mathrm{G}$.

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Kazutoshi KARIYAMA. "Classification of Very Cuspidal Representations of $\mathrm{GL}_m(D)$." Tokyo J. Math. 42 (1) 285 - 327, June 2019. https://doi.org/10.3836/tjm/1502179296

Information

Published: June 2019
First available in Project Euclid: 18 July 2019

zbMATH: 07114910
MathSciNet: MR3982059
Digital Object Identifier: 10.3836/tjm/1502179296

Subjects:
Primary: 22E50

Rights: Copyright © 2019 Publication Committee for the Tokyo Journal of Mathematics

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Vol.42 • No. 1 • June 2019
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