Recordings of the online video training sessions.
Go to the online training page.
Here are the slides from the session and the terminal output.
- Welcome. Questions: Ordering of the KGB elements, closure relations of corresponding orbits, Hasse diagram for G=Sp(4,R).
- Slides, cont'd. More on discrete series parameters for Sp(4,R). Distinguished fiber. Borel subgroups containing the compact Cartan and corresponding discrete series.
- Examples using the software: SL(2,R), x=0->x=1, lambda->-lambda via W. Commands "print_KGB", "block_of", "show", "hc_parameter".
- 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.
- G=Sp(6,R): Choice of x with prefered simple roots. "distinguished_fiber", "rho_K".
- KGB on other Cartan subgroups. G= Sp(4,R). "print_real_Weyl", KGB orbits of the real Weyl group.
- Preview for next time: General parameters: intermediate Cartans, cuspidal data, discrete series of levifactors.
Go to part A
Return to online-training page for information about upcoming training sessions.