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ADMISSIBLE REPRESENTATIONS OF GL2(Qp)

 
Acknowledgements
 
Introduction
      Motivation
      Definitions
      The Principal Series
      Supercuspidal Representations
      The Local Langlands Correspondence
      Connection with Modular Forms
      Category
      Verbose Output
 
Creation of Admissible Representations
 
Attributes of Admissible Representations
 
Structure of Admissible Representations
 
Local Galois Representations
 
Examples
 
Bibliography







DETAILS

 
Introduction

      Motivation

      Definitions

      The Principal Series

      Supercuspidal Representations

      The Local Langlands Correspondence

      Connection with Modular Forms

      Category

      Verbose Output

 
Creation of Admissible Representations
      LocalComponent(M, p) : ModSym, RngIntElt -> RepLoc
      Example RepLoc_creation-example (H139E1)

 
Attributes of Admissible Representations
      CentralCharacter(pi) : RepLoc -> GrpDrchElt
      Conductor(pi) : RepLoc -> RngIntElt
      DefiningModularSymbolsSpace(pi) : RepLoc -> ModSym
      IsMinimal(pi) : RepLoc -> BoolElt, GrpDrchElt, RepLoc
      Example RepLoc_attributes-example (H139E2)

 
Structure of Admissible Representations
      IsPrincipalSeries(pi) : RepLoc -> BoolElt
      IsSupercuspidal(pi) : RepLoc -> BoolElt
      PrincipalSeriesParameters(pi) : RepLoc -> GrpDrchElt, GrpDrchElt
      CuspidalInducingDatum(pi) : RepLoc -> ModGrp

 
Local Galois Representations
      GaloisRepresentation(pi) : RepLoc -> GrpPerm, Map, RngPad, ModGrp
      AdmissiblePair(pi) : RepLoc -> RngPad, Map

 
Examples
      Example RepLoc_example1 (H139E3)
      Example RepLoc_example2 (H139E4)
      Example RepLoc_example3 (H139E5)

 
Bibliography

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