G = E7, adjoint, quaternionic G^v = E7, simply connected, hermitian Note: G is connected type: E7 ad s real form: 2 dual real form: 1 Dynkin Diagram: 2 | 1-3-4-5-6-7 Infinitesimal character of block: rho Special Special Orbit Cells Diagram #R A DualOrbit Cells Diagram #R A E6 0 2022020 1 1 (3A1)'' 2 0000002 4 1 D5 1 2020020 2 1 (A3+A1)'' 1 2000002 4 1 D4 2 2020000 2 1 A5'' 0 2000022 2 1 Fundamental weights lambda_2,lambda_5,lambda_7 are not in root lattice Infinitesimal character of block = rho => allowed infinitesimal characters: #0s on 2,5,7 is even all orbits allowed