Software Tutorial

• Preliminaries
  • Getting started using the software
  • Help files
  • Basic Commands
  • Vectors
  • Matrices
  • Functions and Loops
  • Rational Matrices
  • Local Variables
• Structure Theory
  • Root Data and Lie Types
  • Real Groups
  • atlas choice of coordinates
  • Change of Coordinates
  • Cartan Subgroups
  • Real Forms
• Coordinates and Characters
  • Occurrence Matrices
  • Parameters
  • Parameters for Real Tori
  • The Character Differential
  • Trivial Representation of \(SL(2,R)\)
• First Examples of Representations.
  • Introduction
  • Example \(G=SL(2,\mathbb R)\).
  • Example \(G=PSL(2,\mathbb R)\)
  • Example \(G=Sp(4,\mathbb R)\)
  • Example \(G=SO(3,2)\)
  • More parameter commands
  • Cuspidal Data for Representations
  • Lowest \(K\)-types of a Representation
  • Representations with Zero Infinitesimal Character
  • Translation Principle
  • Blocks of Representations
• \(K\) orbits on \(G/B\).
  • Introduction on \(K\) orbits on \(G/B\)
  • Example: \(SL(2,\mathbb R)\)
  • More on \(K\backslash G/B\)
  • \(K\backslash G/B\) for other Cartan subgroups
• Discrete Series
  • Background
  • Example \(SL(2,R)\)
  • Example \(Sp(4,R)\)
  • Example \(Sp(6,\mathbb R)\)
• General Parameters
  • Introduction
  • Principal Series and Discrete Series revisited
  • General Parameters \(Sp(4,\mathbb R )\)
• Parabolic Induction
  • Real Parabolic Induction
  • Cohomological Parabolic Induction
  • \(A_{\mathfrak q}(\lambda)\) Construction