F₄ · Neutral gradings
16 neutral gradings · KL, Fourier, Arthur packets
| Ambient orbit | KL block sizes | Arthur parameters | Parameters in packets | Graded orbits | Local systems |
|---|---|---|---|---|---|
| 1 | 1 × 1 | 1 | 1 | 1 | 1 |
| A₁ | 2 × 2 | 2 | 2 | 2 | 2 |
| \tilde A₁ | 4 × 4 | 3 | 4 | 3 | 4 |
| A₁ + \tilde A₁ | 5 × 5 | 4 | 5 | 4 | 5 |
| \tilde A₂ | 3 × 3 | 2 | 2 | 3 | 3 |
| A₂ | 7 × 7 | 5 | 7 | 5 | 7 |
| A₂ + \tilde A₁ | 8 × 8 | 4 | 6 | 6 | 8 |
| \tilde A₂ + A₁ | 6 × 6 | 4 | 4 | 6 | 6 |
| B₂ | 8 × 8 | 2 | 4 | 6 | 8 |
| C₃(a₁) | 10 × 10 | 6 | 8 | 8 | 10 |
| F₄(a₃) | 19 × 19, 1 × 1 | 11 | 19 | 12 | 20 |
| C₃ | 8 × 8 | 2 | 2 | 8 | 8 |
| B₃ | 10 × 10 | 2 | 2 | 8 | 10 |
| F₄(a₂) | 18 × 18 | 6 | 8 | 14 | 18 |
| F₄(a₁) | 20 × 20 | 2 | 4 | 16 | 20 |
| F₄ | 16 × 16 | 2 | 2 | 16 | 16 |
Counting conventions
Matrix dimensions are listed separately for each block. Parameters in packets counts distinct IC parameters, without multiplicities or repeated membership. Local systems counts orbit–local-system pairs across all exported series. “Not computed” means that the selected export does not contain that result, rather than a count of zero.