Software · Archive
Online training: session 3, part B (March 15, 2016)
Archived page from the old site: recordings of the online training sessions held in February–March 2016. The embedded player of the old page no longer works; the links below open the recordings on YouTube.
Recordings of the online video training sessions. Go to the online training page.
Here are the slides from the session and the terminal output.
Watch the recording on YouTube. The topics below link to the point in the recording where each begins.
- 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.
Return to online-training page for information about upcoming training sessions.