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ON THE EXISTENCE OF ADMISSIBLE SUPERSINGULAR REPRESENTATIONS OF $p$-ADIC REDUCTIVE GROUPS

Published online by Cambridge University Press:  13 January 2020

FLORIAN HERZIG
Affiliation:
Department of Mathematics, University of Toronto, 40 St. George Street, Room 6290, Toronto, ON M5S 2E4, Canada; herzig@math.toronto.edu
KAROL KOZIOŁ
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI48109-1043, USA; kkoziol@umich.edu
MARIE-FRANCE VIGNÉRAS
Affiliation:
Institut de Mathématiques de Jussieu, 4 place Jussieu, 75005 Paris, France; marie-france.vigneras@imj-prg.fr

Abstract

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Suppose that $\mathbf{G}$ is a connected reductive group over a finite extension $F/\mathbb{Q}_{p}$ and that $C$ is a field of characteristic $p$. We prove that the group $\mathbf{G}(F)$ admits an irreducible admissible supercuspidal, or equivalently supersingular, representation over $C$.

Type
Number Theory
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2020

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ON THE EXISTENCE OF ADMISSIBLE SUPERSINGULAR REPRESENTATIONS OF $p$-ADIC REDUCTIVE GROUPS
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