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# Branching Rules for Ramified Principal Series Representations of $\mathrm{GL}(3)$ over a $p$-adic Field

Published:2009-12-04
Printed: Feb 2010
• Peter S. Campbell,
University of Bristol, UK
• Monica Nevins,
University of Ottawa, Canada
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## Abstract

We decompose the restriction of ramified principal series representations of the $p$-adic group $\mathrm{GL}(3,\mathrm{k})$ to its maximal compact subgroup $K=\mathrm{GL}(3,R)$. 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 representations, branching rules, maximal compact subgroups, representations of $p$-adic groups
 MSC Classifications: 20G25 - Linear algebraic groups over local fields and their integers 20G05 - Representation theory

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