Generic Stabilizers for Simple Algebraic Groups

We prove a myriad of results related to the stabilizer in an algebraic group G generic vector representation V over algebraically closed field k. Our are on level schemes, which carries more information than considering both Lie algebra and G(k) k-points. For simple faithful irreducible, we existence general position, sometimes called principal orbit type. determine those for position is smooth, or dimV/G<dimG, there v∈V whose trivial.