liegr.. _session_3B:
Online Training Session 3, Part B
=====================================
1. Questions
----------------
Welcome. Questions: Ordering of the KGB elements, closure relations of corresponding orbits, Hasse diagram for G=Sp(4,R).
.. raw:: html
2. More Slides
----------------
Slides, cont'd. More on discrete series parameters for Sp(4,R). Distinguished fiber. Borel subgroups containing the compact Cartan and corresponding discrete series.
.. raw:: html
3. Examples Using the Software
------------------------------------
Examples using the software: SL(2,R), x=0->x=1, lambda->-lambda via W. Commands "print_KGB", "block_of", "show", "hc_parameter".
.. raw:: html
4. :math:`Sp(4,\mathbb{R})`
----------------------------------
Sp(4,R). How to identify each discrete series. Commands "all_discrete_series_gamma", "K_0", "status_texts". Parameters associated to a KGB element and HC parameter: "discrete_series"; "generate_W", "cross" (cross action of W on KGB elements. Stabilizer in W of a KGB element). Other choices of K<->KGB elements.
.. raw:: html
5. :math:`Sp(6,\mathbb{R})`
---------------------------------
G=Sp(6,R): Choice of x with prefered simple roots. "distinguished_fiber", "rho_K".
.. raw:: html
6. KGB on other Cartans
---------------------------
KGB on other Cartan subgroups. G= Sp(4,R). "print_real_Weyl", KGB orbits of the real Weyl group.
.. raw:: html
7. Preview for Next Time
-----------------------------
Preview for next time: General parameters: intermediate Cartans, cuspidal data, discrete series of levifactors.
.. raw:: html