Online Training Session 3, Part A

1. Welcome Back

Welcome. New features in atlas software. Use of git. Instructions on Atlas website.

2. More on Software Syntax

More software syntax: use of set and ”:=”. ratmat.at file, rational_inverse, show, ratmat_as_mat. Local variables in strings of functions, use of ”;”.

3. More Principle Series Examples

The all_parameters.at file. More Principal series examples, minimal_principal_series and all_minimal_principal_series commands for non-semisimple and non-split groups.

4. Representations Attached to Given Cartans

Representations attached to a given Cartan and infinitesimal character/differential: all_parameters_Cartan_gamma; all_parameters.

5. Slides: KGB Parameters

Slides on K\G/B parameters: (x,lambda,nu). Case: G has discrete series = distinguished involution is I.

6. Slides: Finiteness of KGB

Slides, continued: Finiteness of KG/B. Parameter set for KG/B.

7. Slides: \(SL(2,\mathbb{R})\) Example

8. Slides: continued