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Branching Rules for Ramified Principal Series Representations of GL(3) over a p-adic Field

Part of: Linear algebraic groups and related topics

Published online by Cambridge University Press:  20 November 2018

Peter S. Campbell  and
Monica Nevins
Peter S. Campbell
Affiliation:
Department of Mathematics, University of Bristol, UK, e-mail: peter.campbell@bristol.ac.uk
Monica Nevins
Affiliation:
Department of Mathematics and Statistics, University of Ottawa, e-mail: mnevins@uottawa.ca
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Abstract

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We decompose the restriction of ramified principal series representations of the $p$-adic group $\text{GL}\left( 3,\,\text{k} \right)$ to its maximal compact subgroup $K\,=\,\text{GL}\left( 3,\,\mathcal{R} \right)$. Its decomposition is dependent on the degree of ramification of the inducing characters and can be characterized in terms of filtrations of the Iwahori subgroup in $K$. We establish several irreducibility results and illustrate the decomposition with some examples.

Keywords

principal series representationsbranching rulesmaximal compact subgroupsrepresentations of p-adic groups

MSC classification

Secondary: 20G25: Linear algebraic groups over local fields and their integers 20G05: Representation theory
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 62 , Issue 1 , 01 February 2010 , pp. 34 - 51
Copyright
Copyright © Canadian Mathematical Society 2010

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