ORBITS OF VECTORS IN SOME REPRESENTATIONS. Ⅰ

摘要

Let Φ be a root system of type E_6, E_7, or E_8. Let K be a field of characteristic different from 2. Let S be the maximal root of Φ and Φ_0 = { a ∈ Φ;δ ⊥ a}. The orbits of the group G_(sc)(Φ_0,K) acting on the set are described.