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

  Published:2005-06-01
 Printed: Jun 2005
  • Monica Nevins
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Abstract

We explicitly describe the decomposition into irreducibles of the restriction of the principal series representations of $SL(2,k)$, 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 $SL(2,k)$ in terms of the restrictions of its irreducible constituents to a maximal compact subgroup.
Keywords: representations of $p$-adic groups, $p$-adic integers, orbit method, $K$-types representations of $p$-adic groups, $p$-adic integers, orbit method, $K$-types
MSC Classifications: 20G25, 22E35, 20H25 show english descriptions Linear algebraic groups over local fields and their integers
Analysis on $p$-adic Lie groups
Other matrix groups over rings
20G25 - Linear algebraic groups over local fields and their integers
22E35 - Analysis on $p$-adic Lie groups
20H25 - Other matrix groups over rings
 

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