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Recordings of the online video training sessions.
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- 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].
Go to part A
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