Online Training Session 4, Part B

1. $SO(4,2)$

G=SO(4,2) Block of the tivial. Cuspidal Levi factors of G.

2. $SO(5,1)$

G=SO(5,1) Only one conjugacy class of Cartan subgroups.

3. $Sp(4,\mathbb{R})$

G=Sp(4,R) Inducing from DS vs inducing from other irreducibles.

4. $SL(2,\mathbb{R})$

G=SL(2,R) Composition Series, Character formulas. KL_P and KL_Q polynomials and KL matrix.

5. $Sp(4,\mathbb{R})$

G=Sp(4,R) KL matrix. KL polynomials and Jantzen filtration.

6. $SO(4,4)$

G=SO(4,4)

7. $PSO(4,4)$, $Spin(4,4)$

PSO(4,4), Spin(4,4). block_sizes matrix, Triality, Vogan duality.

8. $Sp(8,\mathbb{R})$

Sp(8,R) Block sizes matrix, real forms, dual group real forms, Vogan duality.