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 (H152E1)

 
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 (H152E2)

 
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 -> GalRep
      AdmissiblePair(pi) : RepLoc -> RngPad, Map

 
Examples
      Example RepLoc_example1 (H152E3)
      Example RepLoc_example2 (H152E4)
      Example RepLoc_example3 (H152E5)

 
Bibliography

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