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Branching Rules for Ramified Principal Series Representations of GL(3) over a p-adic Field
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- Journal:
- Canadian Journal of Mathematics / Volume 62 / Issue 1 / 01 February 2010
- Published online by Cambridge University Press:
- 20 November 2018, pp. 34-51
- Print publication:
- 01 February 2010
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- Article
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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.
Branching Rules for Principal Series Representations of SL(2) over a p-adic Field
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- Journal:
- Canadian Journal of Mathematics / Volume 57 / Issue 3 / 01 June 2005
- Published online by Cambridge University Press:
- 20 November 2018, pp. 648-672
- Print publication:
- 01 June 2005
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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.
