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Branching Rules for Principal Series Representations of SL(2) over a p-adic Field

Published online by Cambridge University Press:  20 November 2018

Monica Nevins
Monica Nevins*
Affiliation:
Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, K1N 6N5, e-mail: mnevins@uottawa.ca
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Abstract

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We explicitly describe the decomposition into irreducibles of the restriction of the principal series representations of $SL\left( 2,\,k \right)$, for $k$ a $p$-adic field, to each of its two maximal compact subgroups (up to conjugacy). We identify these irreducible subrepresentations in the Kirillov-type classification of Shalika. We go on to explicitly describe the decomposition of the reducible principal series of $SL\left( 2,\,k \right)$ in terms of the restrictions of its irreducible constituents to a maximal compact subgroup.

Keywords

20G2522E3520H25representations of p-adic groupsp-adic integersorbit methodK-types
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 57 , Issue 3 , 01 June 2005 , pp. 648 - 672
Copyright
Copyright © Canadian Mathematical Society 2005

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