Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-10T20:08:16.588Z Has data issue: false hasContentIssue false
  • English
  • Français

LOCALLY ANALYTIC CUSPIDAL REPRESENTATIONS FOR $\mathrm{GL}_2$ AND RELATED GROUPS

Published online by Cambridge University Press:  15 February 2006

Mark Kisin  and
Matthias Strauch
Mark Kisin
Affiliation:
Department of Mathematics, University of Chicago, 5734 South University Avenue, Chicago, IL 60637, USA (kisin@math.uchicago.edu)
Matthias Strauch
Affiliation:
Mathematisches Institut, Einsteinstraβe 62, 48149 Münster, Germany (straucm@math.uni-muenster.de)
Get access Rights & Permissions [Opens in a new window]

Abstract

For a finite extension $F/\mathbb{Q}_p$ we construct and study a class of locally analytic representations of GL$_2(F)$ and related groups such as the quaternion algebra over $F$. The construction is based on inducing a locally analytic character of a maximal torus. We show that for a generic character the resulting representation is topologically irreducible, and not isomorphic to a locally analytic principal series, when the torus is non-split.

Keywords

locally analyticcuspidal representation$p$-adic groupPrimary 22E50Secondary 11F85
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 5 , Issue 3 , July 2006 , pp. 373 - 421
Copyright
2006 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)