.. _session_2A: Online Training Session 2, Part A ================================== 1. New Features on Website ---------------------------- Welcome back. New features in Atlas website. Other videos. .. raw:: html 2. Questions from Session 1 -------------------------------- Questions from last time. Coordinates in atlas, change of coordinates matrix, the coordinates.at file. Newest version of atlas-scripts. .. raw:: html 3. Cartans ---------------- Cartans of different real forms. G= SO(5,4). occurrence_matrix .. raw:: html 4. Parameters -------------------- Parameters.Parameter space, irreducible and standard modules. Langlands parameters. .. raw:: html 5. Example: :math:`SL(2,\mathbb{R})` ------------------------------------------- Example: SL(2,R). The command "all_parameters_gamma" .. raw:: html 6. Characters of Tori ------------------------- Characters of real tori. The command "torus". Components of the characters: {theta, gamma, lambda} and {theta,lambda,nu}. Example: Characters of :math:`T=S^1`. Equivalent parameters. .. raw:: html 7. :math:`T = \mathbb{R}^x` ----------------------------------- Example: Characters of T=R^x. .. raw:: html 8. :math:`T = \mathbb{C}^x` ------------------------------ Example: Characters of T=C^x .. raw:: html 9. Differential ------------------------ Differential in terms of lambda and nu. The functions ``x(parameter)``, ``lambda(parameter)``, ``nu(parameter)``, ``involution(x)`` .. raw:: html 10. Trivial Representation of :math:`SL(2,\mathbb{R})` -------------------------------------------------------------- Example: trivial representation of SL(2,R) .. raw:: html 11. Preview: KGB Orbits ----------------------------- Preview: x --> K orbit on G/B. .. raw:: html