Software · Archive
Online training: session 2, part B (March 1, 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.
Watch the recording on YouTube. The topics below link to the point in the recording where each begins.
- Welcome Back. Summary of previous hour.
- Minimal Principal Series of split groups. SL(2,R) example. Use of functions KGB(RealForm,int)->KGBElt, involution(KGBElt)->mat, all_parameters_gamma(RealForm,ratvec->[Param]), Induced representations: I(Param)->(Param,string), composition_series(Param)->ParamPol, show(ParamPol)->void, parameter(KGBElt,ratvec,ratvec)->Param.
- More functions: cuspidal_data(Param)->(([int],KGBElt),Param).
- G=PSL(2,R), parameters, composition series. Parameters of trivial rep; is_finite_dimensional(Param)->bool, dimension(Param)->int.
- G=Sp(4,R). Principal series, tau-invariant: tau(Param)->[int]; listing tau invariants, real roots types r1, r2, rn.
- Question: Can lambda-rho get to the sign/trivial characters on the disconnected part?
- Lowest K types: Principal series for Sp(4,R)
- G=SO(3,2): principal series, tau invariant, composition series
- More on G=Sp(4,R). W-equivalent parameters. The function find([Param],Param)->int.
- G=SL(2,R). Different infinitesimal character. Translation: T(Param,ratvec)->Param; changing both, nu and lambda. Changing nu, fixing lambda.
- G=SP(4,R). Infinitesimal character zero.
- G=Sp(4,R): Blocks: print_block(Param)->void; block_sizes(InnerClass)->mat.
- G=E8. Block sizes, split_form(InnerClass/RootDatum/Lietype)->RealForm; real_forms(InnerClass/CartanClass)->[RealForm].
Return to online-training page for information about upcoming training sessions.