Article contents
Représentations banales de
${\rm GL}_{m}({\rm D})$
Published online by Cambridge University Press: 02 January 2013
Abstract
Let ${\rm F}$ be a non-Archimedean locally compact field of residue characteristic
$p$, let
${\rm D}$ be a finite-dimensional central division
${\rm F}$-algebra and let
${\rm R}$ be an algebraically closed field of characteristic different from
$p$. We define banal irreducible
${\rm R}$-representations of the group
${\rm G}={\rm GL}_{m}({\rm D})$. This notion involves a condition on the cuspidal support of the representation depending on the characteristic of
${\rm R}$. When this characteristic is banal with respect to
${\rm G}$, in particular when
${\rm R}$ is the field of complex numbers, any irreducible
${\rm R}$-representation of
${\rm G}$ is banal. In this article, we give a classification of all banal irreducible
${\rm R}$-representations of
${\rm G}$ in terms of certain multisegments, called banal. When
${\rm R}$ is the field of complex numbers, our method provides a new proof, entirely local, of Tadić’s classification of irreducible complex smooth representations of
${\rm G}$.
MSC classification
- Type
- Research Article
- Information
- Copyright
- Copyright © 2013 The Author(s)
References
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