Prehomogeneous Spaces Associated with Nilpotent Orbits in Type Eii

Nilpotent orbits in type EII Orbit KC diagram i dim g i C ∩ kC Highest weights of gC ∩ kC 1. d 0 d 0 d 1 d 0 d 0 d 1 1 10 (1, 0, 0, 0, 1, 0) (0, 0, 0, 0, 0, 2) 2. d 1 d 0 d 0 d 0 d 1 d 2 1 8 (1, 0, 0, 1,−1, 0) (−1, 1, 0, 0, 1, 0) 2 2 (1, 0, 0, 0, 1, 0) (0, 0, 0, 0, 0, 2) 3. d 0 d 1 d 0 d 1 d 0 d 0 1 8 (1, 0, 1,−1, 0, 0) (0,−1, 1, 0, 1, 0) 2 4 (1, 0, 0, 0, 1, 0) 4. d 0 d 0 d 1 d 0 d 0 d 3 1 9 (1, 0, 0, 0, 1, 0) 3 1 (0, 0, 0, 0, 0, 2)