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