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

Part of: Representation theory of groups Discontinuous groups and automorphic forms Lie groups

Published online by Cambridge University Press:  13 January 2020

FLORIAN HERZIG ,
KAROL KOZIOŁ  and
MARIE-FRANCE VIGNÉRAS
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 $C$.

MSC classification

Primary: 22E50: Representations of Lie and linear algebraic groups over local fields
Secondary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields 20C08: Hecke algebras and their representations
Type
Number Theory
Information
Forum of Mathematics, Sigma , Volume 8 , 2020 , e2
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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