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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 ([email protected])
Matthias Strauch
Affiliation:
Mathematisches Institut, Einsteinstraβe 62, 48149 Münster, Germany ([email protected])
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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

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